Preheat oven to 350°F.

In a medium mixing bowl, whisk together the milk and egg.

Cut the chicken breasts into 1-inch pieces and add to the milk and egg mixture.

Spray a 9x13-inch baking dish with nonstick cooking spray and set aside. Mix the breadcrumbs, salt, and pepper together, then pour onto a large plate. Using a slotted spoon, remove the chicken pieces from the egg mixture and transfer to the seasoned breadcrumbs. Toss with the spoon to fully coat the chicken pieces with the breadcrumbs, then arrange in an even layer in the prepared baking dish

Arrange the cubed ham and cheese over the breaded chicken pieces.

In a small mixing bowl, whisk together the cream of chicken soup and milk.

Pour the soup mixture over the chicken, ham, and cheese. Cover the dish with aluminum foil.

Bake the casserole on middle rack of oven for 35 minutes.

Carefully remove the foil and continue baking until chicken is cooked through and top is lightly browned, about 10 minutes.

Check to see that casserole is done. Remove from oven or add time as needed.

Serve immediately. Leftovers can be stored in an airtight container for up to 1 week.