Cook pasta according to package instructions, then drain.

While pasta is boiling, cut the broccoli florets and tender stems into 1 - 2 inch pieces.

Heat oil and butter in a heavy skillet over medium, then add the broccoli, garlic, salt, pepper and cayenne pepper.

Sautee for 3-4 minutes, until broccoli turns bright green and gets some brown edges

Add an inch of water to the pan of broccoli, then cover and cook for another 5 minutes.

Drain any remaining water from the broccoli, then toss in the cooked pasta.

Transfer to a serving dish and top with grated cheese.