I discovered a robe sleeve that had what looked like a 3 inch wide cuff only it was a band of material sewn to the end of the sleeve then turned so that it is on the outside of the sleeve then sewn to it with piping in the edge. I can't decide whether I need to cut the fake cuff in a rectangle like a regular cuff and cut the curve off the sleeve or something else. I've played with cutting a wide piece of fabric using the same shape as the sleeve end but when I fold it over to the right side of the sleeve piece it doesn't want to lay as flat as I think it should.

If anyone can figure out what I'm after from this, I would appreciate any suggestions you may have.

I believe I understand what you would like, Simply trace the stitch line of the hem shape on the upper end of your "cuff piece" squaring off the lower edge. Cut two,for a lined cuff and stitch around three sides right sides together, leaving the upper edge unstitched, turn, press and stitch one edge to the sleeve bottom.
Machine or Hand catch stitch the inner edge. (Think of it like applying a collar with an under and over collar.)

Kaaren