You can load a double-struck or outline font of your choice and use its symbols as delimiters.
\documentclass{article}
\tracinglostchars=2
\usepackage{unicode-math}
% Font available from:
% https://www.fontsquirrel.com/fonts/library-3-am
\setfontface\outline{LIBRARY 3 AM}[
Scale=MatchUppercase]
\newcommand\llparen{\mathopen{\textnormal{\outline (}}}
\newcommand\rrparen{\mathclose{\textnormal{\outline )}}}
\newcommand\llbrack{\mathopen{\textnormal{\outline [}}}
\newcommand\rrbrack{\mathclose{\textnormal{\outline ]}}}
\newcommand\llbrace{\mathopen{\textnormal{\outline \textbraceleft}}}
\newcommand\rrbrace{\mathclose{\textnormal{\outline \textbraceright}}}
\newcommand\Parens[1]{%
\llparen%
#1%
\rrparen}
\newcommand\Brackets[1]{%
\llbrack%
#1
\rrbrack}
\newcommand\Braces[1]{%
\llbrace%
#1%
\rrbrace}
\pagestyle{empty} % Format the MWE for TeX.SX
\begin{document}
\begin{gather}
\llbrace\llbrack\llparen \mathbb R \rrparen\rrbrack\rrbrace \
\Braces{\Brackets{\Parens{\mathbb C}}}
\end{gather}
\end{document}

This template does not enable scaling, which would be much more complicated. Unfortunately, although you can set a blackboard font with \setmathfontface, unicode-math will not substitute it for (), {} or [].
You could, however, define \bigllparen, \biggrrbrace, etc., which scale the delimiters, and build size-changing commands from that.
$\llparenthesis x \rrparenthesis$or$\left(\!\left(\frac{1}{\frac{1}{2}}\right)\!\right)$work? – M. Al Jumaily Jul 14 '20 at 02:29\leftand\rightdirectives. In this regard, the macros\llparenthesisand\rrparenthesisof thestmaryrdorstixpackages are very different from\llbracketand\rrbracket. – Mico Jul 15 '20 at 18:50