Bring a large pot of salted water to a rolling boil. Add the broccoli florets and cook for approximately 5 minutes, or until they become tender.

Transfer the cooked broccoli to a bowl. Reserve ½ cup of the broccoli cooking liquid for the sauce before proceeding.

Warm the olive oil in a skillet over medium heat. Add the minced garlic and crushed red pepper flakes, then stir in the cooked broccoli along with the reserved broccoli water.

Season the mixture with salt and freshly ground black pepper. Cook for about 10 minutes, stirring from time to time, until the broccoli softens enough to be gently mashed with a spoon.

Return to the same pot of broccoli water and add the shell pasta. Cook according to the package directions until the pasta is al dente, then drain well.

Place the drained pasta into the skillet with the softened broccoli mixture. Add the grated Parmesan cheese and stir thoroughly until the pasta is evenly coated.

If the sauce feels too thick, loosen it with a small splash of reserved pasta water until the desired texture is reached.

Taste and adjust the seasoning with additional salt and black pepper as needed. Serve immediately with extra Parmesan cheese sprinkled over the top.