Take one slice of bread and layer it with one slice of cheese, a slice of ham, and a slice of turkey. Add another slice of cheese on top before placing the second slice of bread to complete the sandwich.
In a shallow dish, whisk together the eggs, milk or cream, salt, and pepper until combined.
Carefully dip the assembled sandwich into the egg batter, coating both sides fully but avoiding soaking it too long to prevent sogginess.
Heat butter in a skillet over medium heat. Place the battered sandwich in the skillet and fry for approximately 3 to 4 minutes on each side until the bread is golden brown and crispy, and the cheese inside has melted thoroughly.
Transfer the sandwich to a plate and, if desired, dust lightly with powdered sugar. Serve alongside raspberry or strawberry jam for dipping.
