How to Make It
In a large skillet, melt the butter. Add the turnips and cook over moderately high heat until lightly browned in spots, about 4 minutes. Add the chicken broth, thyme and sugar, cover and simmer over low heat until the turnips are tender, about 30 minutes. Using a slotted spoon, transfer the turnips to a bowl. Discard the thyme sprigs.
Boil the pan juices over high heat until thickened slightly, about 2 minutes. Season the turnips with salt and pepper. Pour the pan juices over the turnips, toss with currants and serve.