Preheat your oven to 350°F (180°C).
In a large mixing bowl, combine the shredded chicken, broccoli florets, sliced carrots, and cooked rice.
In another bowl, mix together the cream of chicken soup, milk, garlic powder, onion powder, salt, and black pepper. Stir until smooth.
Pour the soup mixture over the chicken and vegetables. Add half of the cheddar cheese and mix well until all ingredients are combined.
Transfer the chicken mixture to a greased 9x13-inch baking dish, spreading it evenly.
In a small bowl, combine the bread crumbs, olive oil, and remaining cheddar cheese. Mix until bread crumbs are coated.
Sprinkle the bread crumb mixture evenly over the casserole.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
After 30 minutes, remove the foil and bake for an additional 15 minutes, or until the top is golden brown and the casserole is bubbly.
Once done, remove from the oven and let it cool for a few minutes before serving. Optionally, garnish with fresh parsley.