Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the cooked chicken, steamed broccoli, cooked brown rice, cheddar cheese, cream of chicken soup, milk, garlic powder, onion powder, black pepper, and salt. Mix well until all ingredients are evenly coated.
Transfer the mixture to a greased 9x13 inch baking dish, spreading it out evenly.
In a small bowl, mix the breadcrumbs with the olive oil until the breadcrumbs are well coated. Sprinkle the breadcrumb mixture evenly over the casserole.
Bake in the preheated oven for 25-30 minutes, or until the casserole is bubbly and the breadcrumbs are golden brown.
Remove from the oven and let it cool for about 5 minutes before serving.