Knocking-out an outline on a surface to leave a hole

I’ve made the cutting outline on a surface, but how to knock-out the unwanted material in the middle, so as to create a hole? Should I extrude to form a brep and then subtract or might there be a simpler way?

Cookie cutter not cutting.gh (16.7 KB)

Thank you!

Split Brep workes also with your curve or your brep as a cutter.