Fill a large pot with water, adding a pinch of salt, and bring it to a boil. Add the broccoli florets and cook for 2-5 minutes. Reserve ½ cup of the broccoli water, then transfer the broccoli to a bowl.

In a large skillet, heat olive oil over medium heat. Add minced garlic and red pepper flakes, stirring for about 30 seconds until fragrant. Stir in the cooked broccoli and reserved water, seasoning with salt and pepper. Cook for about 10 minutes until broccoli is tender.

In the same pot with broccoli water, bring to a boil and add pasta. Cook according to package instructions until al dente, usually 8-10 minutes. Drain and reserve additional water if needed.

Add the drained pasta to the skillet with the broccoli mixture. Fold in grated Parmesan cheese and stir until combined, adding reserved pasta water if needed for consistency.

Taste and adjust seasoning as needed, then serve immediately with extra Parmesan on top.