Spread 1 side of each bread slice with mustard. Layer 6 bread slices, mustard side up, with 1 ham slice, 1 cheese slice, and another ham slice; top with remaining bread slices, mustard side down.
Whisk together eggs and milk in a shallow dish until blended. Dip each sandwich into egg mixture, coating both sides.
Place sandwiches 2 inches apart on a lightly greased baking sheet. Place another lightly greased baking sheet, greased side down, on top of sandwiches.
Bake at 475° for 15 to 20 minutes or until golden brown. Serve immediately.