Heat a large covered pot of water. When the water comes to a rapid boil, add the pasta, stir, and cover the pot until the water boils again.
Meanwhile, in a large skillet, saute the broccoli and garlic in olive oil until the garlic is golden, but not brown, and the broccoli is bright green and crisp-tender. Add plenty of freshly ground black pepper. Pour a couple of spoonfuls of pasta water into the skillet to steam the broccoli. When the pasta is al dente, drain it and put it into warmed serving dishes.
Top it with the broccoli mixture and the grated "cheese". Drizzle on a little olive oil, if you would like. Serve immediately.
Serves 4.
