Bring a large pot of salted water to a rolling boil. Add the broccoli florets and cook for 5 minutes until they turn bright green and tender when pierced with a fork. Use a slotted spoon to transfer the broccoli to a bowl, then measure out 1/2 cup of the cooking water and set aside.

Heat olive oil in a large skillet over medium heat. Add the minced garlic and red pepper flakes, stirring constantly for 30 seconds until fragrant but not browned. Immediately add the cooked broccoli and the reserved 1/2 cup broccoli water to stop the garlic from burning. Season with salt and pepper.

Cook for 10 minutes, stirring occasionally. As the broccoli softens, use the back of your spoon to mash it into chunky pieces that will create a rustic sauce. The water will reduce and thicken, creating a creamy base.

While the broccoli simmers in the skillet, bring the pot of broccoli cooking water back to a boil. Add the pasta and cook until al dente, about 8-10 minutes. Before draining, use a measuring cup to scoop out 1 cup of the starchy pasta water and set aside. Drain the pasta thoroughly.

Add the drained pasta directly to the skillet with the broccoli mash. Toss everything together, adding half the Parmesan cheese while stirring. If the sauce seems thick, add the reserved pasta water one tablespoon at a time until you reach a silky consistency that coats the shells.

Taste and adjust seasoning with additional salt and pepper if needed. Serve immediately, topped with the remaining Parmesan cheese.