Cook pasta al dente according to package directions. Drain and set aside.
While pasta cooks, add cream, butter, salt and pepper to the skillet. Bring to a simmer.
Mix the cooked pasta, broccoli, and chicken in the cream mixture. Add parsley flakes if desired.
Serve immediately with extra cheese as desired.
Notes
Frozen or fresh broccoli would work equally well. Do no overcook the broccoli; reheating in the creamed mixture will add a little bit of cooking time. Or, substitute peas for the broccoli if preferred. No need to pre-cook frozen peas, as the creamed mixture will cook it quickly.