Place each piece of chicken between 2 sheets of wax paper; flatten to 1/4-inch thickness using a meat mallet or rolling pin. Sprinkle with salt and pepper. Combine eggs and milk; brush chicken pieces with milk mixture. Place ham slice and cheese slice in center of each chicken piece. Brush top of cheese slices with milk mixture. Fold short ends of chicken over ham and cheese; roll up, beginning with one unfolded side. Secure with wooden picks. Dredge chicken in flour; dip in remaining milk mixture, and coat well with bread crumbs. Cover and chill 1 hour. Heat 1/2 inch oil in a heavy skillet (3500F); add chicken, and pan-fry over medium heat 20 minutes or until golden brown, turning servings.
Mushroom Sauce Combine all ingredients; cook over medium heat, stirring