Step 1Peel the turnips and cut into quarters, leaving the stems attached. Place the turnips in a large skillet with one-half cup water, the butter, shallot and salt. Stir well, cover tightly and place over medium-high heat. Cook until the turnips just begin to become tender but are still slightly crisp, 8 to 10 minutes.
Step 2Remove the lid and increase the heat to high. Let the liquid boil off and continue cooking, without stirring, until you see the bits that are stuck to the bottom of the pan begin to brown. Add the walnuts, stir and continue cooking until the turnips are covered in an irregular brown glaze, 8 to 10 minutes.
Step 3Add the sherry vinegar. Stir to mix well and scrape up some of the brown glaze from the bottom of the pan (you won't get it all). Serve immediately.