Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with olive oil.
In a large mixing bowl, combine the cooked turkey, broccoli florets, cooked brown rice, cheddar cheese, cream of mushroom soup, milk, garlic powder, onion powder, black pepper, and salt. Mix well until all ingredients are evenly coated.
Pour the mixture into the prepared baking dish, spreading it out evenly.
If using breadcrumbs, sprinkle them evenly over the top of the casserole for added crunch.
Bake in the preheated oven for 25-30 minutes, or until the casserole is bubbly and the top is golden brown.
Remove from the oven and let it cool for 5 minutes before serving.