Heat oven to 400°F. Cook the pasta according ot the package directions. Reserve 3/4 cup of the cooking water, drain the pasta and return to the pot.
Meanwhile, on a rimmed baking sheet, toss the broccoli, nuts, oil, garlic, 1/2 tsp salt, and 1/4 tsp pepper. Roast, tossing once, until the broccoli is tender, 18-20 minutes.
Toss the pasta with the broccoli mixture, butter, and 1/2 cup of the reserved pasta water. (Add more water if the pasta seems dry.)