Minimum size of brackets using \left and \right

Question

I would like to use brackets in math mode which stretch automatically like \left( and \right), but have a given minimum size, for example:

Using something like \delimitershortfall and \delimiterfactor does not work well because it stretches all brackets (including the ones which are already big enough). I would just like to put a limit on the minimum size of the brackets.

How can I achieve this?

Minimal working example:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

How it works:
\begin{align}
    x &= \left( 2 + y \right)\\
    y &= \left( \sum_n \frac{n}{2} \right)
\end{align}

How I would like it to work:
\begin{align}
    x &= \Big( 2 + y \Big)\\
    y &= \left( \sum_n \frac{n}{2} \right)
\end{align}

\end{document}

Answer 1

It looks much nicer with the original small size but

\left(\strut2...

will force the bracket to be at least the size forced by \strut

or replace \strut by \rule{0pt}{20pt} for a specific min height

\documentclass{article}
\usepackage{amsmath}

\begin{document}

How it works:
\begin{align}
    x &= \left( 2 + y \right)\\
    y &= \left( \sum_n \frac{n}{2} \right)
\end{align}

How I would like it to work:
\begin{align}
    x &= \Big( 2 + y \Big)\\
    y &= \left( \sum_n \frac{n}{2} \right)
\end{align}

with rule:
\begin{align}
    x &= \left( \rule{0pt}{11.5pt}2 + y \right)\\
    y &= \left( \sum_n \frac{n}{2} \right)
\end{align}

without left/right
\begin{align}
    x &= (2 + y )\\
    y &= \Bigl( \sum_n \frac{n}{2} \Bigr)
\end{align}
\end{document}