Cut the greens from the turnips. Wash the greens in a basin of cold water, lift out, and set aside. Cut the turnips into halves or quarters so they are all roughly the same size. Rinse and drain.
Melt the butter in a large heavy-bottomed pot. Add the turnips and season with salt and pepper. Let the turnips simmer over medium heat for a minute or so without browning, then add a glass of water and put on the lid. Cook for 4 to 5 minutes, until turnips are just tender. Add the greens and cook for 2 minutes more.