Hakurei turnips are a small, delicately flavored Japanese variety that will win over even the harshest turnip critic. If you can't find them, use another small turnip like the Tokyo, or substitute with red radishes. Lo advocates using the whole turnip, from bitter, leafy-green tops to sweet roots.
Place turnips in a large skillet; add water to cover turnips halfway. Add butter, sugar, and a large pinch of salt; bring to a boil. Cook, stirring occasionally, until liquid is syrupy and turnips are tender, about 15 minutes.
If turnips are tender before liquid has reduced, use a slotted spoon to transfer turnips to a plate and reduce liquid until syrupy. Return turnips to pan and stir to coat well.
Add turnip greens to skillet and cook over medium heat, stirring occasionally, until just wilted, 2-3 minutes. Season with salt.
DO AHEAD: Can be made 4 hours ahead. Let stand at room temperature. Rewarm before continuing.