Begin by cooking the pasta according to package instructions in a large pot of salted boiling water. Add the broccoli florets to the pot during the last 2 minutes of cooking, then drain both the pasta and broccoli together. Set aside.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant but not browned.
Pour in the heavy cream and bring to a gentle simmer. Stir in the grated Parmesan cheese, mixing until melted and combined into a creamy sauce.
If you like a little heat, add the red pepper flakes at this stage, along with salt and pepper to taste.
Add the cooked pasta and broccoli to the creamy sauce, tossing well to coat all the ingredients. Allow cooking for an additional 1-2 minutes, until everything is heated through.
Serve immediately, garnished with freshly chopped parsley for a pop of color and freshness.