Heat oven to 400° F. Cook the pasta according to the package directions. Reserve ¾ cup of the cooking water. Drain the pasta and return it to the pot.
Meanwhile, on a rimmed baking sheet, toss the broccoli and onion with the oil, ½ teaspoon salt, and ¼ teaspoon pepper. Nestle the sausage among the vegetables.
Roast, tossing once, until the broccoli is tender and the sausage is cooked through, 18 to 20 minutes.
Toss the pasta with the broccoli and sausage mixture, butter, and ½ cup of the reserved cooking water (add more if the pasta seems dry).
Sprinkle the pasta with Parmesan before serving.