Obviously, the state of the art is Power Tools. I'd say one of these bits, probably something around the 5/8" size with single-cut blades, in an angle-head die grinder, would make quick work of hollowing out your turnip.

Alternately, if you don't really want the state of the art that badly, a set of yard-sale-grade wood-carving chisels would probably work well. The ones that have J-hook-shaped ends for carving out holes would likely be particularly useful.