Heat oven to 400 degrees F. Bring a large pot of salted water to a boil.
Combine broccoli, garlic, walnuts, salt and pepper in a medium-size bowl. Drizzle with olive oil and stir until coated. Place broccoli mixture on a large rimmed baking sheet and roast at 400 degrees F for 13 minutes, stirring twice.
Cook pasta following package directions, about 10 minutes. Drain and return to pot.
Add broccoli mixture to pasta pot and stir in broth, butter and Parmesan cheese. Serve immediately.