Cook the pasta. Meanwhile, in a large 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 and tender. Add plenty of freshly ground black pepper. Pour a couple of spoonfuls of pasta water into the skillet to steam the broccoli while it's sautéing.

When the pasta is done, drain it and put it into warmed serving dishes. Top it with the broccoli mixture and grated cheese. Drizzle on a little extra-virgin olive oil if you like. Serve immediately.