Cook the pasta according to package instructions until al dente, then drain and set aside.
In a large skillet over medium heat, heat the olive oil. Add the chorizo and cook until browned, about 5-7 minutes.
Add the minced garlic and red pepper flakes to the skillet and sauté for about 1 minute until fragrant.
Stir in the broccoli florets and cook for about 3-4 minutes until tender-crisp.
Pour in the heavy cream and bring the mixture to a gentle simmer.
Mix in the pasta and Parmesan cheese, tossing well to combine. If needed, add reserved pasta water to loosen the sauce.
Season with salt and pepper to taste before serving.