Cook the penne pasta according to package instructions until al dente. Add the broccoli florets to the boiling pasta water during the last 2 minutes of cooking. Drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the diced chicken and season with salt and pepper. Cook for about 5-7 minutes, or until the chicken is cooked through and no longer pink.
Add the minced garlic to the skillet and sauté for 1-2 minutes until fragrant.
Pour in the heavy cream and bring to a gentle simmer. Stir in the Italian seasoning, mozzarella cheese, and Parmesan cheese until melted and well combined.
Add the cooked penne and broccoli to the skillet, tossing everything together until evenly coated in the creamy sauce.
Cook for an additional 2-3 minutes to heat through. Adjust seasoning with more salt and pepper if needed.
Serve hot, garnished with fresh parsley.