Step 1Bring a large pot of liberally salted water to a rolling boil. Add the pasta and cook until just tender, about 7 minutes, depending on the pasta.
Step 2Meanwhile, heat the olive oil and prosciutto in a large skillet over medium heat until the prosciutto loses its color, 3 to 4 minutes. Add the diced turnips and cook until they begin to turn golden, about 10 minutes; stir occasionally, but not too often or you'll delay the browning.
Step 3When the turnips are beginning to brown, add the greens and the garlic and stir together. Add the white wine and cook until it evaporates, about 1 minute. Continue cooking, stirring, about 5 minutes.
Step 4When the pasta is done, drain it, reserving one-half cup cooking water. Add the pasta and the reserved water to the skillet with the turnips and greens. Increase the heat to high and cook, stirring constantly, until the liquid is reduced to a light sauce, about 2 to 3 minutes. Taste and add salt if necessary.
Step 5Divide among 6 heated serving bowls and serve immediately sprinkled with the grated cheese.