**Cook the Pasta:** Bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Reserve 1/2 cup of pasta water, then drain and set aside.

**Cook the Chicken:** In a large skillet, heat olive oil or butter over medium heat. Add the cubed chicken, season with salt, pepper, and Italian seasoning, and cook until golden and cooked through. Remove the chicken from the skillet and set aside.

**Sauté Garlic and Broccoli:** In the same skillet, add a bit more oil if needed. Sauté the minced garlic for about 30 seconds until fragrant, then add the broccoli florets. Cook for 4-5 minutes until the broccoli is tender but still crisp.

**Prepare the Sauce:** Reduce heat to low. Stir in the heavy cream, chicken broth, and Parmesan cheese, mixing until the cheese is melted and the sauce is creamy. Add reserved pasta water as needed to adjust the consistency.

**Combine Everything:** Return the chicken to the skillet and toss in the cooked pasta. Mix well to coat everything in the creamy sauce. Adjust seasoning with salt and pepper.

**Serve:** Serve hot, garnished with additional Parmesan cheese or red pepper flakes if desired.