Meanwhile, in a large cast iron skillet, sauté 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 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 grated cheese.  Drizzle on a little extra virgin oil if you like.