Bring a large pot of water to a boil. Add the penne, and cook at a rolling boil until the pasta is just tender. Drain, rinse under cold water, drain again, and reserve.
Cut the broccoli florets into fairly small pieces. Reserve the stems for another use. Bring a large saucepan of water to a boil. Add the broccoli, and simmer for 2 minutes. Drain, rinse under co