Preheat oven to 375°F.
Steam or microwave broccoli until slightly tender but not mushy.
In a saucepan, melt butter and whisk in cream cheese until smooth.
Pour in heavy cream and stir until creamy.
Add garlic powder, onion powder, paprika, salt, and pepper.
Stir in ½ cup cheddar and ½ cup mozzarella until melted.
Combine chicken, broccoli, and the sauce in a large bowl.
Spread mixture into a baking dish and top with remaining cheese.
Bake 20–25 minutes until golden, bubbling, and slightly browned on top.
Rest 5 minutes before serving.