Prepare the oven: Preheat oven to 375°F (190°C). Lightly grease a 9×13-inch baking dish.
Prepare the broccoli: Steam or blanch fresh broccoli until just tender. If using frozen broccoli, thaw and drain thoroughly.
Sauté the aromatics: Melt butter in a large skillet over medium heat. Add onion and cook for 3–4 minutes. Add garlic and cook for 30 seconds.
Make the sauce: Stir in flour and cook for 1 minute. Gradually whisk in chicken broth and milk. Cook, stirring frequently, until slightly thickened.
Add cheese and seasonings: Reduce heat to low. Stir in sour cream and 1½ cups Cheddar until melted. Add salt, pepper, garlic powder, and paprika.
Combine: Stir the cooked rice, chicken, and broccoli into the cheese sauce until evenly coated.
Assemble: Transfer the mixture to the prepared baking dish. Sprinkle with remaining Cheddar. Add breadcrumbs on top if desired.
Bake: Cover loosely with foil and bake for 20 minutes. Remove foil and bake another 10–15 minutes, until hot and bubbling and the cheese is melted.
Brown the top: For a golden topping, broil for 1–2 minutes, watching carefully.
Rest and serve: Let the casserole rest for 5–10 minutes before serving.