Spread mustard over each bread slice and layer in the following order: bread, cheese, ham and turkey; repeat meats and cheese once more then top with remaining bread slice
Meanwhile, heat oil in a large skillet or griddle over medium heat
Whisk eggs and milk in a shallow bowl
Dip each side of each sandwich in the egg mixture
Cook, pressing the sandwiches with a sheet of vegetable spray-coated foil weighted with a skillet, until golden brown, about 3 minutes per side