Cook the pasta in a large pot of salted boiling water until al dente. Drain and set aside.
In a skillet, heat olive oil over medium heat. Add garlic and sauté until fragrant.
Add the chicken and broccoli, stirring until warmed through.
Pour in the cream and let it simmer for 3 to 4 minutes, then stir in parmesan cheese.
Season with salt, black pepper, and red pepper flakes if using.
Toss the cooked pasta with the sauce until evenly coated. Serve warm with extra parmesan.