Melt the butter in a saucepan over medium heat. Cook the chicken, mixed vegetables, and potatoes until warmed through, about 5-7 minutes.
Warm the chicken and mushroom soups in a separate pot over medium-low heat. Pour in the milk and stir constantly until heated through, about 3 minutes. Pour the soup mixture into the chicken mixture.
Open one can of crescent roll dough and fit it into a 9Ă—13-inch baking dish. Pinch the seams together. Pour the filling. Top it with the 2nd can of crescent roll dough.
Cover the dish loosely with foil. Bake it for 45 to 50 minutes or until the crust is golden brown.