Cook the penne pasta according to package instructions. In the last 3 minutes of cooking, add the broccoli florets to the boiling water. Drain and set aside.

In a large skillet, heat 2 tablespoons of olive oil over medium heat. Add the chicken pieces, season with salt, pepper, Italian seasoning, and red pepper flakes. Cook until the chicken is browned and cooked through, about 6-8 minutes. Remove the chicken from the skillet and set aside.

In the same skillet, add the remaining tablespoon of olive oil and minced garlic. Sauté for 1-2 minutes until fragrant, being careful not to burn the garlic.

Pour in the heavy cream and bring to a simmer. Stir in the mozzarella and Parmesan cheese until melted and smooth. Season with additional salt and pepper to taste.

Add the cooked pasta, broccoli, and chicken back into the skillet. Toss everything together until well combined and heated through.

Serve immediately, garnished with fresh parsley.