Heat 2 tablespoons of butter in a 10-inch ovenproof skillet over medium heat. Add broccoli and sauté for 4 minutes until tender. Remove broccoli to a bowl.
Melt the remaining butter in the skillet. Add garlic and cook for 1 minute until fragrant.
Add cream, simmer, and reduce by half (3–5 minutes). Stir in ½ cup mozzarella and all the Parmesan until melted.
Season with salt and pepper, then add broccoli and chicken. Stir to combine.
Top with the remaining 1 cup of mozzarella cheese.
Preheat broiler and place the skillet 6 inches from the heat source. Broil for 2–5 minutes until the cheese browns.
Serve warm and enjoy!