Extracting pull quote

Following up on [https://github.com/erusev/parsedown/issues/348)]

I too would like to style pull quotes separately, which effectively means copying the contents between the two markers (in the OP case $$$) and duplicating those in a structure like

<aside class="pullquote">
   duplicated text
</aside>

How could I do that? Or maybe it is already possible, in which case a pointer would be very welcome.