Cook the pasta according to package instructions, drain, and set aside.
In a large pan, heat olive oil over medium heat and sauté garlic until fragrant.
Add cooked chicken and broccoli, stirring for about 2-3 minutes.
Pour in the heavy cream and bring to a gentle simmer.
Stir in Parmesan cheese, salt, black pepper, and red pepper flakes.
Add the cooked pasta to the sauce and toss to combine.
Serve warm with extra Parmesan cheese on top.