In a shallow dish, whisk together the eggs, milk, vanilla extract, and ground cinnamon until well combined.
Lay out the slices of bread on a clean surface.
Spread a thin layer of raspberry jam on one side of each bread slice.
Place 2 slices of ham, 2 slices of turkey, and 2 slices of Swiss cheese on four of the bread slices with the jam.
Top each sandwich with another bread slice, jam side down, to complete the sandwiches.
Heat a large skillet or griddle over medium heat and lightly grease it with butter.
Dip each sandwich into the egg mixture, making sure to coat both sides evenly. Allow any excess egg mixture to drip off.
Carefully place the dipped sandwiches onto the preheated skillet or griddle.
Cook each side for 3-4 minutes, or until golden brown and the cheese is melted.
Remove the sandwiches from the heat and let them cool slightly.
Optional: Dust the sandwiches with powdered sugar for a touch of sweetness.
Serve the Monte Cristo sandwiches warm with maple syrup or additional raspberry jam for dipping, if desired. Enjoy!