Heat the oven to 400°F and lightly grease a 9-by-13-inch baking dish. Cut each chicken breast into approximately three large pieces, pounding very thick pieces to an even thickness if needed.

Crush the Ritz crackers and combine them with the salt, black pepper, and dried parsley. Place the milk, shredded cheddar, and seasoned cracker crumbs in three separate shallow bowls.

Dip each chicken piece in the milk, press it firmly into the cheddar, and then coat it with the cracker crumbs. Arrange the pieces in the prepared baking dish and sprinkle any remaining cheese or crumbs over the top.

Cover the dish tightly with foil and bake for 35 minutes. Remove the foil and continue baking for 10 minutes, until the coating is crisp and the thickest chicken piece reaches 165°F internally.

Combine the cream of chicken soup, sour cream, and butter in a small saucepan. Heat over medium heat, stirring until smooth and hot, but do not allow the sauce to boil vigorously.

Serve the baked chicken warm with the creamy sauce spooned over each portion. Add a little extra dried parsley if desired.