This recipe from Southern Living was designed for hakurei turnips, but you can that purple-top turnip into bite-size chunks and treat it the same way.
3 tablespoons unsalted butter, divided 15 small turnips, cut in half lengthwise, greens removed 3 tablespoons apple cider vinegar Water Salt 2 tablespoons honey
Heat a 12-inch ovenproof skillet over medium-high heat 5 minutes. Melt 2 tablespoons butter in skillet and add turnips, cut side down. Cook, without turning, 4 minutes or until golden. Add vinegar and enough water to come to a total depth of 1/4-inch. Sprinkle with salt. Bring to a boil, cover and reduce heat to medium-low. Cook 5 minutes or until turnips are tender. Increase heat to medium-high, uncover and boil until liquid is almost evaporated. Lower heat slight and continue to cook until liquid is gone. Add honey and remaining tablespoon butter and serve.