Cook the penne pasta according to package instructions until al dente.
While the pasta cooks, heat olive oil in a large skillet over medium heat.
Season the chicken breasts with salt and pepper, then add to the skillet.
Remove the cooked chicken from the skillet and let it rest before slicing.
In the same skillet, add minced garlic and sauté until fragrant, about 30 seconds.
Add broccoli florets to the skillet and cook for 3-4 minutes until bright green and tender-crisp.
Pour in the heavy cream and bring it to a simmer, stirring frequently.
Stir in the grated Parmesan cheese and mix until melted and smooth.
Slice the rested chicken and add it to the sauce along with the cooked penne.
If the sauce is too thick, add reserved pasta water to reach the desired consistency.
Serve the chicken and broccoli pasta warm, garnished with extra Parmesan if desired.
