Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions until al dente. During the last 3 minutes of cooking, add the broccoli florets to the pot with the pasta.
Reserve 1 cup of pasta water, then drain the pasta and broccoli, setting them aside.
In the same pot, heat the olive oil over medium heat. Add the minced garlic and red pepper flakes, cooking until the garlic is fragrant and lightly golden, about 1-2 minutes.
Return the pasta and broccoli to the pot with the garlic oil. Pour in the lemon juice and zest, and toss until everything is well combined. If the mixture seems dry, gradually add reserved pasta water until desired consistency is achieved.
Stir in the grated Parmesan cheese and season with salt and pepper to taste. Toss well until the cheese has melted and the pasta is coated.
Serve hot, garnished with fresh basil leaves and additional Parmesan cheese on top.