Preheat oven to 350°F (175°C). Grease a 9x13-inch baking dish.
Stir chicken, ham, hash browns, soup, sour cream, milk, 1 1/2 cups cheddar, garlic powder, onion powder, salt, and pepper in a large bowl.
Spread the mixture evenly in the prepared baking dish.
Sprinkle the remaining 1/2 cup cheddar over the top.
Mix crushed cornflakes or crackers with melted butter, then scatter over the casserole.
Bake 40-45 minutes, until hot, bubbly, and golden on top.
Let the casserole rest 5-10 minutes before serving.