Bring a large pot of salted water to a boil.
Add the shell pasta and cook according to package instructions until al dente.
In the last 3 minutes of pasta cooking, add the broccoli pieces to the boiling water.
While pasta and broccoli cook, heat olive oil in a large skillet over medium heat.
Add minced garlic and crushed red pepper to the skillet and sauté for 1-2 minutes until fragrant.
Drain the pasta and broccoli, reserving 1/2 cup of the pasta water.
Add the drained pasta and broccoli to the skillet with garlic and pepper.
Toss everything together, adding reserved pasta water gradually to create a light sauce.
Season with salt and black pepper to taste.
Remove from heat and stir in the freshly grated parmesan cheese until well combined.
Serve immediately with extra parmesan if desired.