Think prop spinner for a model airplane.
Assuming that I'm not making it out of spun metal, the obvious way to proceed is to turn the outside (or inside), then flip the thing over and turn the inside (or outside). Turning the first side is obvious -- but how to hold the work to do the opposite side? Turn the inside, then turn the base of the outside, then make a mandrel that holds the base while I finish turning the nose piece?