Preheat the oven to 375°F (190°C).
In a large mixing bowl, combine the cooked chicken, cooked rice, and broccoli florets.
In a separate bowl, whisk together the milk, sour cream, melted butter, garlic powder, onion powder, salt, and pepper.
Pour the milk mixture over the chicken, rice, and broccoli mixture and stir until well combined.
Transfer the mixture to a greased casserole dish and spread it out evenly.
In a small bowl, combine the shredded cheddar cheese, grated Parmesan cheese, and breadcrumbs. Sprinkle the cheese and breadcrumb mixture on top of the casserole.
Bake in the preheated oven for 35-40 minutes or until the casserole is heated through and the cheese is melted and golden brown.
Remove from the oven and let it cool for a few minutes before serving.
Serve hot and enjoy!