Melt butter in a large, heavy skillet over medium heat. Add chopped broccoli, cook and stir till crisp tender, about 4-5 minutes. Remove broccoli from skillet.
Turn skillet to low heat, add garlic and saute for 60 seconds. Stir in the cream, parmesan, salt, pepper, and 1/2 cup of the mozzarella cheese. Cook and stir till melted and creamy.
Return broccoli to the sauce with the diced chicken. Cook and stir till heated through. Add more salt and pepper if desired.
Sprinkle remaining shredded mozzarella cheese over the top. Place the pan on the top oven rack and broil for 3-4 minutes or until cheese is lightly browned.
Notes
Instead of browning the cheese, you can just turn the skillet heat down to low, cover the skillet, and simmer for 5 minutes or until cheese is melted.