Preheat oven to 425 degrees F. Spray a 9x13-inch baking dish with nonstick cooking spray; set aside. Whisk together egg and egg whites in a small bowl; set aside. Combine bread crumbs and parmesan cheese in a small bowl; set aside.
Lightly pound chicken until equal in thickness and season with salt and pepper, to taste. Place a slice of ham and half slice of cheese on top of each chicken breast.
Roll up each chicken breast, dip in egg wash, roll in crumb mixture then place seam side down in prepared pan. Spray the tops of chicken with nonstick cooking spray.
Bake for 25-30 minutes, or until cooked through or until it reaches an internal temperature of 165 degrees F.