In a bowl, whisk together the eggs, milk, nutmeg, salt, pancake mix and vanilla extract until smooth.
For the sandwiches, place a slice of both cheese on each side of the bread. Add the turkey & ham slices in the center of the sandwich. If you like Dijon mustard you can spread a thin layer of that on one side of the bread. Close the sandwiches.
Heat a flat griddle to medium heat. Add a little butter to the griddle and when it's hot, dip one sandwich at a time on both sides (like french toast) into the egg mixture and place the sandwich onto the griddle. Cook until lightly golden brown on both sides and until the cheese is melted. Remove sandwich from the grill and dust with powdered sugar. Serve with your favorite berry jam.