Preheat your oven to 400°F (200°C). Grease a 9x13-inch baking dish.
Crush the crackers into fine crumbs and mix in the salt, pepper, and parsley.
Cut each chicken breast into 3 large chunks.
Dip each piece in milk, then coat it in grated cheese (press it on well), and finally roll it in the cracker crumbs.
Place the coated chicken pieces into the baking dish.
Melt the butter and drizzle it over the top of the chicken.
Cover the dish with foil and bake for 35 minutes. Remove the foil for the last 10 minutes to crisp things up.
While it bakes, whisk together the soup and sour cream in a small saucepan and warm over low heat.
Serve the crispy chicken hot with a generous spoonful of the creamy sauce.