Bring a large pot of salted water to a boil for the Fusilli.
Meanwhile, heat the oil in a large, heavy skillet. Add the bacon and saute over medium heat until it just begins to brown. Add the radicchio and stir-fry for a few minutes, until it begins to wilt. Add a few tablespoons water and continue to cook the radicchio and bacon together until the radicchio is tender.
When the water for the pasta is boiling, add the fusilli and cook it about 8 minutes, until it is al dente. Drain it well, then transfer it to the skillet with the radicchio and bacon and toss them together. Add the butter.
Serve at once with grated cheese on the side.