Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the cooked turkey, broccoli florets, cooked brown rice, shredded cheddar cheese, cream of mushroom soup, milk, garlic powder, onion powder, salt, and black pepper. Mix until well combined.
Transfer the mixture to a greased 9x13-inch baking dish, spreading it evenly.
In a small bowl, mix the breadcrumbs with olive oil until they are evenly coated. Sprinkle the breadcrumb mixture 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 5 minutes before serving.