What physical feature must a nonstick skillet possess to aid in cleanly sliding out the finished omelette?

Gently sloped sides.

The geometry of the cooking vessel is crucial for the final movements involved in plating an omelette, especially the challenging French roll. A pan designed for omelettes must feature sides that gently slope outward rather than being steeply vertical. These gentle slopes create an inclined plane that allows the relatively soft, cooked egg mass to slide easily toward the lip of the pan without catching, tearing, or requiring excessive maneuvering with a utensil. A pan with sharp, vertical sides would trap the edges of the egg, making the extraction and subsequent rolling or flipping process unnecessarily difficult.