1. Cook the pasta according to the package instructions. Drain and set aside.
2. Steam the broccoli florets until tender, about 5 minutes.
3. In a blender, combine the steamed broccoli, basil leaves, Parmesan cheese, toasted pine nuts, garlic, and olive oil. Blend until smooth. Season with salt and pepper to taste.
4. Toss the cooked pasta with the broccoli pesto until well coated.
5. Serve immediately, garnished with extra Parmesan cheese if desired.