Bring a large pot of salted water to a boil. Add the spaghetti and cook according to package instructions.

During the last 2 minutes of cooking, add the broccoli florets to the pot. Drain the pasta and broccoli in a colander.

In a skillet, heat the olive oil over medium heat. Add the minced garlic and red pepper flakes, sautéing until fragrant, about 1 minute.

Remove from heat and stir in the lemon zest and juice.

Add the drained pasta and broccoli to the skillet, tossing to coat in the sauce. Season with salt and black pepper to taste.

Serve immediately, topped with grated parmesan cheese.