Preheat the oven to 350°F.
In a large mixing bowl, combine the cooked chicken, steamed broccoli, cheddar cheese, cream of chicken soup, sour cream, garlic powder, onion powder, salt, and black pepper. Mix until well combined.
Transfer the mixture to a greased 9x13 inch baking dish.
In a separate bowl, mix the breadcrumbs with olive oil until evenly coated. Sprinkle the breadcrumb mixture over the chicken and broccoli mixture in the baking dish.
Bake in the preheated oven for 25-30 minutes, or until the top is golden brown and the casserole is heated through.
Let it cool for 5 minutes before serving.