Boil the water: Begin by bringing a large stockpot of salted water to a boil over high heat.
Cook the broccoli: Once the water has reached a rolling boil, add the broccoli florets. Stir to ensure the broccoli is evenly submerged. Cook for approximately 3 minutes or until tender. Use a slotted spoon or spider strainer to transfer the broccoli to a food processor, leaving the boiling water in the stockpot.
Cook the pasta: Add the uncooked pasta to the boiling water and cook until al dente. While the pasta cooks, prepare the pesto.
Prepare the pesto: In the food processor, combine the basil, Parmesan, pine nuts, spinach, garlic, lemon zest, lemon juice, salt, and pepper. Pulse the ingredients together while gradually drizzling in the olive oil, processing until smooth. Scoop out ΒΌ cup of the pasta water and add it to the pesto mixture. Continue to pulse until the pesto is creamy and smooth. If needed, add more pasta water to achieve the desired consistency.
Toss the pasta: Once the pasta reaches al dente, reserve an additional 1/2 cup of the pasta water and set it aside. Drain the pasta and return it to the stockpot. Pour the pesto over the pasta and toss to combine. If the pesto appears too thick, gradually add some of the reserved pasta water until you achieve the ideal texture.
Serve: Serve the pasta warm, garnished with additional Parmesan cheese and a twist of freshly ground black pepper. Enjoy!