Bring a large pot of salted water to a boil. Add the penne pasta and cook according to package instructions until al dente. In the last 3 minutes of cooking, add the broccoli florets. Drain and set aside.
While the pasta is cooking, heat olive oil in a large skillet over medium heat. Season the chicken breasts with salt and pepper on both sides and add them to the skillet. Cook for about 6-7 minutes per side or until fully cooked and no longer pink in the center.
Remove the cooked chicken from the skillet and let it rest for a few minutes before slicing it into bite-sized pieces.
In the same skillet, add minced garlic and sauté for about 30 seconds until fragrant.
Pour in the heavy cream and bring to a gentle simmer. Stir in the grated Parmesan cheese until melted and combined. Season with salt, pepper, and Italian seasoning if using.
Add the drained penne and broccoli to the skillet, tossing everything together to coat in the creamy sauce. Finally, add the sliced chicken back into the skillet.
Give it a final stir, taste, and adjust seasoning if needed. Serve hot, garnished with fresh parsley.