1. Preheat oven to 400°.
2. Cook the pasta according to the package directions. Reserve 3/4 cup of the cooking water, drain the pasta, and return to the pot.
3. Toss together broccoli and next 5 ingredients (through pepper) on a rimmed baking sheet. Roast, tossing once, 18–20 minutes or until the broccoli is tender.
4. Toss the pasta with the broccoli mixture, butter, and 1/2 cup reserved pasta water. (Add more water if the pasta seems dry.) Sprinkle with Parmesan cheese before serving.