Preheat the oven to 400 degrees.

Beat the eggs and milk in a shallow dish. Heat a large pan or skillet over medium-high heat and melt one tablespoon of butter when hot.

Dip a piece of bread into the egg and milk batter for a few seconds. Use a fork or tongs to flip the bread over and coat the other side. Drip off any excess, then place in the hot pan. Repeat with the remaining bread, fitting as many pieces in the skillet as you can at a time. Cook each slice for about 3-4 minutes or until golden brown. Flip the bread over and cook the other side. Repeat with the additional bread, adding more butter to the pan as needed. Place the cooked pieces on a baking sheet.

In a small bowl, stir together the mustard and jam. Spread this evenly over each slice of French toast. Place a slice of Swiss cheese on each. Then add two slices of turkey, two slices of ham, and another slice of cheese to each sandwich. Top with the remaining bread.

Place the sandwiches on the baking sheet. Bake for 10 minutes or until the cheese is sufficiently melted and the sandwich is warmed through. Slice the sandwiches in half and serve hot.