Cook the Pasta and Broccoli:
Bring a pot of salted water to a boil. Add pasta and cook according to package instructions. Add broccoli florets during the last 3 minutes of cooking. Drain, reserving ¼ cup pasta water.
Sauté Garlic:
Heat olive oil in a skillet over medium heat. Add minced garlic and cook for 30 seconds, until fragrant.
Combine:
Add cooked pasta and broccoli to the skillet. Pour in reserved pasta water and sprinkle parmesan cheese. Toss until creamy and coated.
Season and Serve:
Season with salt, pepper, and a squeeze of lemon juice if desired. Serve warm, topped with extra cheese or chili flakes.