Cook the penne pasta in boiling salted water until al dente, then drain and set aside.
In a large skillet over medium heat, add olive oil. Season the chicken breasts with salt and pepper, then cook for about 6-7 minutes per side until golden brown. Remove from skillet and let rest before chopping into bite-sized pieces.
In the same skillet, add broccoli florets and minced garlic; sauté for about 4-5 minutes until bright green.
Pour in heavy cream and chicken broth, bringing to a gentle simmer. Stir in Parmesan cheese until melted.
Return chopped chicken to the skillet along with the cooked penne; gently mix until well coated in sauce.
Serve with additional Parmesan cheese on top if desired.