Cook the pasta according to package instructions until al dente. In the last 3 minutes of cooking, add the broccoli florets to the boiling water with the pasta.

Drain the pasta and broccoli, and set aside.

In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for 1-2 minutes until fragrant.

Pour in the heavy cream and bring to a simmer. Reduce heat to low and stir in the sharp cheddar cheese and Parmesan cheese until melted and smooth.

Add the cooked pasta and broccoli to the cheese sauce, tossing to coat all the ingredients evenly.

Season with salt, pepper, and red pepper flakes if using. Cook for an additional 2-3 minutes until everything is heated through.

Serve immediately, garnished with fresh parsley.