Trim and peel turnips; reserve and chop the greens. Halve turnips. Heat olive oil in a large skillet over medium-high. Add turnips, cut side down; cook 4 minutes or until golden. Turn and add vegetable stock, vinegar, salt, and pepper. Bring to a boil; cover and reduce heat to medium-low. Simmer until turnips are crisp-tender, 5 to 6 minutes. Uncover, increase heat to medium-high, and add greens; cook until liquid reduces by three-fourths and thickens, about 6 minutes. Swirl in butter and honey.