Preheat the oven to 350°F (175°C).
Steam the broccoli florets for 4 to 5 minutes until tender but still crisp. Drain and set aside.
In a medium skillet, melt the butter over medium heat. Add the chopped onion and minced garlic and sauté for 3 to 4 minutes until softened and fragrant. Remove from heat.
In a large mixing bowl, combine the cooked Uncle Ben’s rice, diced cooked chicken, steamed broccoli, sautéed onion and garlic, cream of mushroom soup, sour cream, milk, salt, black pepper, and paprika. Stir until all ingredients are evenly mixed.
Fold in 1/2 cup shredded cheddar cheese and 1/2 cup shredded mozzarella cheese into the mixture.
Transfer the mixture into a greased 9×13 inch casserole dish and spread evenly.
Sprinkle the remaining 1/2 cup cheddar cheese and 1/2 cup mozzarella cheese evenly over the top of the casserole.
Bake uncovered in the preheated oven for 30 to 35 minutes, or until the casserole is heated through and the cheese on top is melted and bubbly.
Remove from the oven and let it rest for 5 minutes before serving.