Preheat the oven to 350° F. Spray a 9x13-inch baking dish with non-stick spray. Lay the chicken pieces evenly into the bottom of the prepared dish.
In a large bowl, whisk a 1/3 cup of the milk and the large egg together until combined. Pour this mixture evenly over the chicken pieces.
Sprinkle the panko breadcrumbs all over the top. Season with salt and pepper. Top the breadcrumbs evenly with the ham and Swiss cheese.
Whisk chicken soup and the remaining 1 cup of milk. Pour mixture evenly over everything. Cover the pan with foil.
Bake for 35 minutes. Remove foil and bake for 10 more minutes. Remove from the oven and let stand for 5 minutes before serving. Serve over cooked egg noodles or rice. Enjoy!