In a large pot of salted boiling water, cook the pasta according to package instructions until al dente. Add the broccoli florets to the pot during the last 2-3 minutes of cooking. Drain the pasta and broccoli and set aside.
In the same pot, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Lower the heat and pour in the heavy cream, stirring well. Gradually add in the shredded cheddar and Parmesan cheese, stirring continuously until the cheeses melt and the sauce becomes smooth and creamy.
Add the drained pasta and broccoli back into the pot, gently tossing everything together until the pasta and broccoli are coated with the creamy cheese sauce.
Season with salt, pepper, and red pepper flakes if using. Allow the pasta to heat through for a minute or two.
Serve immediately, garnished with chopped fresh parsley for an added color and flavor.
Notes
Serve in wide pasta bowls with extra grated cheese on top and a sprinkle of red pepper flakes for color. A slice of crusty bread on the side would complement the dish beautifully!