Beamer: TOC in block

Question

For stylistic reasons (I have everything in blocks), I'd like to have my TOC in a block too, but without having to typset it manually for all sections.

I was surprised that the standard tikz TOC produces garbage when inserted into a block.

Therefore, I tried several methods of building an approximation to the behaviour I'd like (basically like itemize/enumerate), but while I managed to hack something reasonably similar together for the sections, I was unable to get the subsections right at all.

First, I thought it only boils down to knowing exactly which skips to use and how to get them (took me ages to figure the \global stuff out; thanks to https://tex.stackexchange.com/a/43005/42225 and https://tex.stackexchange.com/a/119738/42225), but now I'm finding other strange behaviour (indendation changes for things that are defined exactly the same; can't change font size or color in subsection, etc.), which is why I turn to you, dear TeX.SX.

In the MWE below is a "reference solution" that I'd like to achieve with the standard TOC-functionality. Ideally, they should match exactly, but a few pt's here or there won't hurt anyone. ;-)

\documentclass[10pt]{beamer}

\usepackage[english]{babel}
\usepackage{enumerate}
\usepackage{xparse}

\usetheme{Darmstadt}

\NewDocumentCommand{\mytoc}{O{}}{
\begin{frame}{Test}
\begin{block}{Table of Contents}
    \vskip 6pt % shouldn't be hardcoded...
    \tableofcontents[#1]
\end{block}
\end{frame}
}

%\AtBeginSection{%
%   \mytoc[currentsection]
%}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Begin Document
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}

\begin{frame}{Reference}
\begin{block}{Table of Contents}
\begin{enumerate}[1.]
    \item Motivation
    \item Construction
    \item The Method
    \item Improvements
    \item Applications
    \begin{enumerate}[\theenumi.1.]
        \item One
        \item Two
        \item Three
    \end{enumerate}
\end{enumerate}
\end{block}
\end{frame}

\begin{frame}{Na\"ive version}
\begin{block}{Doesn't work}
\tableofcontents
\end{block}
\end{frame}

\setbeamertemplate{section in toc}{\item[\inserttocsectionnumber.]\inserttocsection}
\begin{frame}{Trying to use itemize}
\begin{block}{Doesn't work}
\begin{itemize}
\tableofcontents
\end{itemize}
\end{block}
\end{frame}

\newlength{\itemsepEnumi}
\newlength{\labelsepEnumi}
\newlength{\parsepEnumi}
\newlength{\topsepEnumi}
\newlength{\partopsepEnumi}
\newlength{\leftmarginEnumi}

\newlength{\itemsepEnumii}
\newlength{\labelsepEnumii}
\newlength{\parsepEnumii}
\newlength{\topsepEnumii}
\newlength{\partopsepEnumii}
\newlength{\leftmarginEnumii}

\newlength{\partopsepEnumz} % z=zero

\begin{frame}{Data Collection}
\begin{block}{Relevant Values} % see tex.stackexchange.com/a/94949/42225
\begin{enumerate}[1.]
  \item \texttt{itemsep}:    \the\itemsep    \global\itemsepEnumi   =\itemsep
                                             \global\labelsepEnumi  =\labelsep
  \item \texttt{parsep}:     \the\parsep     \global\parsepEnumi    =\parsep
  \item \texttt{topsep}:     \the\topsep     \global\topsepEnumi    =\topsep
  \item \texttt{partopsep}:  \the\partopsep  \global\partopsepEnumi =\partopsep
  \item \texttt{leftmargin}: \the\leftmargin \global\leftmarginEnumi=\leftmargin
  \begin{enumerate}[\theenumi.1.]
    \item \texttt{itemsep}:    \the\itemsep    \global\itemsepEnumii   =\itemsep
                                               \global\labelsepEnumii  =\labelsep
                                               \global\parsepEnumii    =\parsep
                                               \global\topsepEnumii    =\topsep
    \item \texttt{partopsep}:  \the\partopsep  \global\partopsepEnumii =\partopsep
    \item \texttt{leftmargin}: \the\leftmargin \global\leftmarginEnumii=\leftmargin
  \end{enumerate}
\end{enumerate}
\global\partopsepEnumz=\partopsep
\end{block}
\end{frame}

\begin{frame}{Data Collection -- Successful}
\begin{block}{Relevant Values}
\begin{enumerate}[1.]
  \item \texttt{itemsep}:    \the\itemsepEnumi
%  \item \texttt{labelsep}:   \the\labelsepEnumi
  \item \texttt{parsep}:     \the\parsepEnumi
  \item \texttt{topsep}:     \the\topsepEnumi
  \item \texttt{partopsep}:  \the\partopsepEnumi
  \item \texttt{leftmargin}: \the\leftmarginEnumi
  \begin{enumerate}[\theenumi.1.]
    \item \texttt{itemsep}:    \the\itemsepEnumii
%    \item \texttt{labelsep}:   \the\labelsepEnumii
%    \item \texttt{parsep}:     \the\parsepEnumii
%    \item \texttt{topsep}:     \the\topsepEnumii
    \item \texttt{partopsep}:  \the\partopsepEnumii
    \item \texttt{leftmargin}: \the\leftmarginEnumii
  \end{enumerate}
\end{enumerate}
%\texttt{partopsep}:  \the\partopsepEnumz
\end{block}
\end{frame}

\setlength{\leftmarginEnumii}{33.3334pt} % how to add skips?

\setbeamertemplate{section in toc}{\leavevmode\leftskip=\leftmarginEnumi%
    \llap{\inserttocsectionnumber.\hspace{\labelsepEnumi}} % why is this automatically blue?
    {\color{black}\smash[b]{\inserttocsection}}\par\vskip\itemsepEnumi}
\setbeamertemplate{section in toc shaded}{\leavevmode\leftskip=\leftmarginEnumi%
    {\color{gray}\llap{\inserttocsectionnumber.\hspace{\labelsepEnumi}}\smash[b]{\inserttocsection}} \par\vskip\itemsepEnumi\vskip\parsepEnumi}
\setbeamertemplate{subsection in toc}{\leavevmode\leftskip=\leftmarginEnumii%
    \llap{%\usetemplate{itemize 2 item} % can't set color/fontsize?!
    \inserttocsectionnumber.\inserttocsubsectionnumber.\hspace{\labelsepEnumii}}
    {\color{black}\smash[b]{\inserttocsubsection}} \par\vskip\itemsepEnumii \vskip\parsepEnumii}
\setbeamertemplate{subsection in toc shaded}{\leavevmode\leftskip=\leftmarginEnumii%
    {\color{gray}\llap{\inserttocsectionnumber.\inserttocsubsectionnumber.\hspace{\labelsepEnumii}}\smash[b]{\inserttocsubsection}} \par\vskip\itemsepEnumii\vskip\parsepEnumii}

\begin{frame}{Trying to Use Skips}
\begin{block}{Doesn't work}
  \vskip\partopsepEnumz % is this the right set/combination of skips?
  \vskip\partopsepEnumi
  \vskip\topsepEnumi
  \tableofcontents
\end{block}
\end{frame}

\begin{frame}{Reference}
\begin{block}{Table of Contents}
\begin{enumerate}[1.]
    \item Motivation
    \item Construction
    \item The Method
    \item Improvements
    \item Applications
    \begin{enumerate}[\theenumi.1.]
        \item One
        \item Two
        \item Three
    \end{enumerate}
\end{enumerate}
\end{block}
\end{frame}

\begin{frame}{Indentation changes from \texttt{section} to \texttt{section shaded}?!}
\begin{block}{Table of Contents}
    \vskip 6pt
    \tableofcontents
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Motivation}
\mytoc[currentsection]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}{Something}
\begin{block}{Something}
Something
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Construction}
\mytoc[currentsection]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}{Something}
\begin{block}{Something}
Something
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{The Method}
\mytoc[currentsection]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}{Something}
\begin{block}{Something}
Something
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Improvements}
\mytoc[currentsection]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}{Something}
\begin{block}{Something}
Something
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Applications}
\subsection{One}
\mytoc[currentsection,currentsubsection]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}{Something}
\begin{block}{Something}
Something
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Two}
\mytoc[currentsection,currentsubsection]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}{Something}
\begin{block}{Something}
Something
\end{block}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Three}
\mytoc[currentsection,currentsubsection]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}{Something}
\begin{block}{Something}
Something
\end{block}
\end{frame}

\end{document}

Answer 1

This is not a perfect match but perhaps it will be close enough to at least give you a basis for further tweaking. Basically, this inserts the block environment into beamer's definition of \tableofcontents and defines a new style my toc for sections/subsections in toc. Because it does not use enumerate, the spacing is not quite the same but this is something you can play with. Also, I have forced the colouring to match an enumeration - I'm not sure if you want this or not but you can easily undo it.

\documentclass[10pt]{beamer}

\usetheme{Darmstadt}

\makeatletter
\def\tableofcontents{\@ifnextchar[{\beamer@tableofcontents}{\beamer@tableofcontents[]}}
\def\beamer@tableofcontents[#1]{%
  \begin{block}{\contentsname}
      \def\beamer@toc@cs{show}%
      \def\beamer@toc@os{show}%
      \def\beamer@toc@css{show}%
      \def\beamer@toc@oss{show}%
      \def\beamer@toc@ooss{show}%
      \def\beamer@toc@csss{show}%
      \def\beamer@toc@osss{show}%
      \def\beamer@toc@oosss{show}%
      \def\beamer@toc@ooosss{show}%
      \beamer@showpartnumber=\c@part%
      \beamer@pausesectionsfalse%
      \beamer@pausesubsectionsfalse%
      \def\beamer@tocsections{<*>}%
      \setkeys{beamertoc}{firstsection=1}%
      \setkeys{beamertoc}{#1}%
      {\makeatletter%
        \pause[0]%
        \@input{\jobname.toc}}%
  \end{block}
  }
\makeatother

\defbeamertemplate{section in toc}{my toc}{%
  \leavevmode\inserttocsectionnumber. {\color{normal text.fg}\inserttocsection}}

\defbeamertemplate{subsection in toc}{my toc}{%
  \leavevmode\leftskip=2.5em{\color{structure.fg}\inserttocsectionnumber.\inserttocsubsectionnumber.} \inserttocsubsection\par}

\setbeamertemplate{sections/subsections in toc}[my toc]

\begin{document}

  \renewcommand*\contentsname{Table of Contents}

  \begin{frame}
    \tableofcontents
  \end{frame}


  \begin{frame}{Reference}
    \begin{block}{Table of Contents}
      \begin{enumerate}[1.]
        \item Motivation
        \item Construction
        \item The Method
        \item Improvements
        \item Applications
        \begin{enumerate}[\theenumi.1.]
          \item One
          \item Two
          \item Three
        \end{enumerate}
      \end{enumerate}
    \end{block}
  \end{frame}

  \section{Motivation}

  \begin{frame}{Something}
    \begin{block}{Something}
      Something
    \end{block}
  \end{frame}

  \section{Construction}

  \begin{frame}{Something}
    \begin{block}{Something}
      Something
    \end{block}
  \end{frame}

  \section{The Method}

  \begin{frame}{Something}
    \begin{block}{Something}
      Something
    \end{block}
  \end{frame}

  \section{Improvements}

  \begin{frame}{Something}
    \begin{block}{Something}
      Something
    \end{block}
  \end{frame}

  \section{Applications}
  \subsection{One}

  \begin{frame}{Something}
    \begin{block}{Something}
      Something
    \end{block}
  \end{frame}

  \subsection{Two}

  \begin{frame}{Something}
    \begin{block}{Something}
      Something
    \end{block}
  \end{frame}

  \subsection{Three}

  \begin{frame}{Something}
    \begin{block}{Something}
      Something
    \end{block}
  \end{frame}

\end{document}

Note that this code does not cover subsubsections, although you could extend it to those if you wished.