Preheat oven to 400 degrees Fahrenheit.
Spray a baking pan with nonstick cooking spray.
Whisk together the egg and ¼ cup milk.
Place the crushed crumbs in a shallow dish and the cheddar cheese in another.
Salt and pepper the chicken breasts, to taste.
Dip the breasts into the egg and milk mixture.
Cover the breasts with shredded cheese using your fingers to press the cheese onto the chicken.
Place breasts into crumbs and cover entirely.
Position chicken onto baking sheet and bake for 30 minutes or until breasts are fully cooked and the centers no longer pink.
While chicken bakes, in a small saucepan, melt the butter and add the chicken soup, sour cream and milk. Whisk together until well-combined and warmed through. Serve sauce over the chicken.