Stir cream of chicken soup, cream cheese, and milk together in a saucepan over medium heat and cook until the cheese is completely melted and the liquid is heated through, about 5 minutes.
Spread hash brown potatoes into a casserole dish; pour soup mixture over the potatoes.
Bake in preheated oven until the edges begin to brown, about 1 hour and 15 minutes.
Sprinkle Cheddar cheese over the dish; let the cheese melt as the dish cools slightly before serving, about 10 minutes.
