Cook the pasta in salted water according to package directions. Add the broccoli during the last 3 minutes of the cooking time.
Heat 2 tablespoons of the butter in a large pan over medium high heat.
Add the chicken to the pan and season with salt and pepper.
Cook the chicken for 5-6 minutes, stirring occasionally, until chicken is browned and cooked through.
Add the garlic and Italian seasoning to the pan and cook for an additional 30 seconds.
Remove the chicken from the pan and cover to keep warm. Wipe out the pan with a paper towel.
Melt the remaining 4 tablespoons of butter in a saucepan over medium low heat.
Add the cream and simmer for 4-5 minutes or until just thickened - do not let it boil.
Whisk in the parmesan cheese, stirring continuously, until cheese has melted.
Season the sauce with salt and pepper to taste.
Place the pasta, broccoli and chicken in the pan with the sauce. Toss to coat. Sprinkle with parsley, then serve.