Bring a 1-gallon pot of water to a boil and add pasta and ½ teaspoon salt. Cook pasta two minutes less than package directions and drain, reserving 2 cups of the cooking water.

In a skillet over medium heat, sauté sliced sausage with 2 tablespoons olive oil until brown, then add garlic and cook one minute. Stir in cooked broccoli.

Toss pasta and broccoli mixture in a skillet with some cooking water until the sauce is coating the pasta and pasta is fully cooked. Season with salt and pepper, to taste.

Stir in Parmesan cheese and top with additional cheese and a pinch of red pepper flakes before serving.