For language learning purposes I would like to use curly brackets with an selection of objects (multiple lines of text, no math environment like this).

But the code
\documentclass[12pt]{extarticle}
\usepackage[a4paper,verbose]{geometry}
\usepackage{fontspec}
\usepackage{empheq}
\setmainfont[Ligatures=TeX]{Gentium Plus}
\begin{document}
I want to buy
\begin{empheq}[left=\empheqlbrace,right=\empheqrbrace]{align*}
tomatoes \\
onions \\
cucumbers
\end{empheq}
in the market.
\end{document}
produces

In addition the words within the brackets should be left aligned.

align*alternates between right and left alignment). You also need something to switch to text mode, like\text{tomatoes}. David used atabularenvironment to perform both of these functions. – Dan Nov 18 '14 at 20:57