Heat oven to 400 degrees. Cook the pasta till al dente, reserving 3/4 cup of the pasta water. Drain the pasta and return it to the pot.
Meanwhile, on a rimmed baking sheet, toss the broccoli and onion with oil, 1/2 tsp salt and pepper. Nestle the sausage in the vegetables and roast, tossing once, until the broccoli is tender and the sausage is cooked through, 18-20 minutes.
Add the sausage mixture, butter and 1/2 cup of the reserved cooking water to the pasta and toss to combine. Sprinkle with the parmesan before serving.