Boil a large pot of salted water for the pasta.
Add the pasta and cook according to package instructions until al dente.
Heat olive oil in a large skillet over medium heat.
Add sliced chicken breasts and season with salt and pepper.
Cook chicken for 5-7 minutes until golden brown and cooked through.
Stir in minced garlic and cook for an additional minute.
Add broccoli florets and cook for 3-4 minutes until bright green.
Pour in heavy cream and stir to combine.
Add grated Parmesan cheese and stir until melted and smooth.
Drain the pasta and toss it in the skillet with the sauce.