Maybe like you sew a welt pocket. But then in the shape of the cut out.
So you sew a piece of fabric on top of your dress, right sides together.
You sew on the lines you want the cut out to look. Then cut out the fabric in the middle, as close to the stitching as possible. You should also snip fabric away around the curved lines.
Then push the piece you stitched on to the inside, wrong side of the dress. Press and that should be it?!
I hope it makes sense! If not, take a look on youtube for welt pockets. You only change the shape, the sewing it on, cutting and pushing it inside is the same.
(I'm Dutch, so it isn't easy to explain it in English)
Let me know it works! Good luck!