Put a large pot of generously salted water over a high flame. Add the broccoli and once the pot is boiling add in the pasta. Cook according to the package instructions minus 2 minutes. The the broccoli will be very fork tender.
When the pot has about 2 minutes to go put a large skillet over a medium flame and heat the oil. Add the garlic and sauté until it just begins to turn golden, about 30 seconds.
Very quickly using a large strainer scoop the pasta and broccoli out of the boiling water and add it to the garlic and oil. Turn the flame up to high and toss well as the broccoli begin to break down. If the pan appears dry add 1/2 cup of the pasta water at a time until you reach the desired consistency. Serve immediately and add cheese at your own risk! :)