Preheat your oven to 350°F. If using olive oil, lightly coat a 9x13-inch baking dish.
In a large bowl, mix together the shredded turkey, broccoli florets, cooked rice, cheddar cheese, cream of mushroom soup, milk, garlic powder, onion powder, salt, and black pepper until well combined.
Pour the mixture into the greased baking dish, spreading it evenly across the bottom. If desired, sprinkle breadcrumbs over the top.
Cover the dish with aluminum foil and bake for 25 minutes.
After 25 minutes, remove the foil and continue baking for another 15 minutes, or until the casserole is bubbling and the top is golden brown.
Allow the dish to rest for about 5 minutes before serving to let the flavors meld.