Boil the water: Bring a large stockpot of salted water to a boil over high heat.
Cook the broccoli: Add the broccoli to the boiling water and cook for 3 minutes, until tender. Use a slotted spoon to transfer the broccoli to a food processor. Keep the water boiling for the pasta.
Cook the pasta: Add the pasta to the same pot and cook until al dente.
Prepare the pesto: To the food processor, add basil, Parmesan, pine nuts, spinach, garlic, lemon zest, lemon juice, salt, and pepper. Blend while drizzling in olive oil until smooth. Add ¼ cup of starchy pasta water and pulse until creamy.
Combine: Drain the pasta, reserving ½ cup of starchy water. Toss the pasta with the broccoli pesto. Add starchy water as needed for a creamy consistency.
Serve: Plate the pasta and garnish with extra Parmesan and freshly-ground black pepper. Serve warm and enjoy!
