1. Cook the broccoli in boiling water until just tender. Drain and set aside. Brown the sausage. Drain off the excess fat. Set aside.
2. Melt the butter in a small saucepan. Add the basil and remove from the heat. Allow to steep for 15 minutes.
3. Cook the pasta in lightly salted boiling water until just soft (about 10 minutes). Drain and return to the pan. Toss in the broccoli, sausage and basil-butter. Reheat slightly. Toss in the cheese and allow it to melt (about 1 minute). Serve warm.