Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions until al dente. During the last 2 minutes of cooking, add the broccoli florets to the pot. Drain the pasta and broccoli in a colander and set aside.
In a large skillet, heat the olive oil over medium heat. Add the sliced chicken and season with salt, pepper, and Italian seasoning. Cook for about 5-7 minutes until the chicken is browned and cooked through.
Add the minced garlic to the skillet with the chicken and sauté for an additional 1-2 minutes until fragrant.
Lower the heat and pour in the heavy cream, stirring to combine. Allow the sauce to simmer for about 2 minutes until slightly thickened.
Stir in the grated Parmesan cheese until melted and combined. If desired, add red pepper flakes for an extra kick.
Add the drained pasta and broccoli to the skillet, tossing everything together until well coated in the creamy sauce. Cook for an additional 1-2 minutes to heat through.
Taste and adjust seasoning with salt and pepper as needed.
Serve hot, garnished with additional Parmesan cheese if desired.