Beat egg and 1/2 cup milk together until combined. Stir in the chicken chunks to coat, then drain, and coat with bread crumbs. Heat oil in a large skillet to 375 degrees F (190 degrees C). Fry breaded chicken cubes in hot oil until golden brown on all sides, then remove, and drain on paper towels.
Place chicken cubes in a glass baking dish, along with the Swiss cheese, and ham. Stir together the soup with 1 cup milk, pour over casserole.
Bake in preheated oven until golden brown and bubbly, about 30 minutes.