Boil the broccoli.
Bring a large pot of salted water to a boil. Add the broccoli florets and cook until tender. Scoop the broccoli out into a bowl and save about 1/2 cup of the cooking water.
Start the sauce base.
Heat the olive oil in a large skillet over medium heat. Add the garlic and crushed red pepper flakes and cook briefly until fragrant.
Mash the broccoli.
Add the cooked broccoli to the skillet along with some of the reserved broccoli water. Season with salt and black pepper, then cook until the broccoli becomes very soft. Mash it gently with a spoon so it turns into a chunky sauce.
Cook the pasta.
In the same pot, cook the shell pasta until al dente according to the package directions. Drain well.
Combine everything.
Add the pasta to the skillet with the broccoli mixture. Stir in the Parmesan until the pasta is coated and glossy. Add a splash of reserved pasta water if you want a looser sauce.
Taste and serve.
Adjust the salt and pepper if needed, then serve right away with extra Parmesan on top.