Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the shredded chicken, steamed broccoli, cheddar cheese, cream of chicken soup, milk, garlic powder, onion powder, black pepper, and salt. Mix until well combined.
Transfer the mixture to a greased 9x13 inch baking dish, spreading it evenly.
In a separate bowl, combine the breadcrumbs and olive oil, mixing until the breadcrumbs are evenly coated.
Sprinkle the breadcrumb mixture evenly 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.
Remove from the oven and let it cool for 5 minutes before serving.