Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the shredded chicken, steamed broccoli, cooked rice, 3/4 cup of the cheddar cheese, cream of chicken soup, milk, garlic powder, onion powder, black pepper, and salt. Mix until well combined.
Transfer the mixture into a greased 9x13 inch baking dish, spreading it evenly.
In a small bowl, combine the breadcrumbs, melted butter, and remaining 1/4 cup of cheddar cheese. Mix until the breadcrumbs are 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 casserole is bubbly and the top is golden brown.
Remove from the oven and let it cool for 5 minutes before serving.