If I got what you ask, in this particular case should be easy:
After activating vertex snapping, select the side profile (which still has the right vertical curvature), and extrude that vertex edge snapping to horizontal edge (which still has horizontal curvature), and in the end you'll cover the entire missing panel.
If you still have original shapes, though, you could also use booleans twice: the first as you did, as "difference", to cut the hole, and another one as "intersect", to get the cut panel as indipendent shape.
Since you like learning new tricks, I'll add another one here below, although I couldn't use it in your specific case, probably due to the specific topology you had in that file.
Here's the trick: if you have a "missing" surface, similar to what you had:
you can sometimes "reconstruct" it using the "grid fill" tool, like this:
which is way more elegant than manually reconstruct it... good to know, I think.