Preheat the oven to 400°. In each of 2 large skillets, melt 2 tablespoons of the butter. Add the turnips to the skillets, flat side down, and season with salt and pepper. Cook over moderately high heat, turning once, until browned, about 3 minutes per side. Transfer the turnips to a bowl.  Scrape the butter from one skillet into the other. Evenly sprinkle the sugar over the butter. Cook over moderate heat until a rich brown caramel forms, 6 minutes. Slowly add the vinegar, taking care that it doesn't bubble over, and stir to dissolve the sugar. Boil over high heat for 2 minutes. Stir in the stock and bring to a boil.  Arrange the turnips in concentric circles in a large, oval baking dish. Pour the caramel over the turnips, top with the thyme and bake for 15 minutes. Baste the turnips. Reduce the oven temperature to 350° and bake for 50 minutes. Baste the turnips again and increase the oven temperature to 400°. Continue baking for 30 minutes longer, or until the turnips are very tender and the caramel mixture has reduced to a glaze. Discard the thyme and serve.