To begin, spread mayonnaise on one slice of bread and mustard on the other. Layer the ham, turkey, and cheese between the bread slices to build a hearty sandwich.
Crack the egg into a shallow bowl and pour in the milk. Whisk together until smooth and well combined to create your dipping mixture.
Gently dip the sandwich into the egg mixture, making sure both sides are well coated. Let the bread absorb the egg wash without getting soggy.
Heat your greased skillet over medium heat and add the sandwich. Cook until each side turns golden brown and the cheese inside melts beautifully.