Place 2 slices of bread on a cutting board. Spread mayonnaise on each slice of bread. Top with a slice of cheese, and 2 slices of ham. Add the second slice of bread and spread with a little bit of mustard if desired. Add 2 slices of turkey and a slice of cheese. Add the 3rd piece of bread.
Using a cutting board or the bottom of a frying pan, gently press the sandwich. Cut off crusts (to help seal the sandwich).
In a small bowl mix together milk, eggs and salt & pepper until combined. Dip sandwich into egg mixture.
Preheat skillet over low heat and add butter. Add sandwich and cook 4-6 minutes. Flip and cook 4-5 minutes more or until cooked through and melted.
(Nutrition information provided is an estimate and will vary based on cooking methods and brands of ingredients used.)