Gather all your ingredients and work area.
In a medium bowl, whisk together eggs, milk, Dijon mustard, salt, and pepper until fully combined.
Lay out four slices of bread and layer two slices each of ham and turkey on top, followed by a slice of Swiss cheese.
Top the sandwiches with the remaining slices of bread, forming four complete sandwiches.
Heat a skillet over medium heat and add a tablespoon of butter.
Dip each sandwich into the egg mixture, ensuring both sides are well-coated before placing them in the skillet.
Cook each sandwich for 3-4 minutes on each side until golden brown and the cheese is melted.
Transfer the finished sandwiches to a plate and keep warm while you repeat with the remaining sandwiches.
Slice the sandwiches in half and serve immediately, optionally with a sprinkle of powdered sugar or a side of your favorite dipping sauce.