Lay out 4 slices of bread on a clean surface. Layer each with turkey, ham, and Swiss cheese. Top with the remaining slices of bread to form sandwiches.
In a large bowl, whisk together the eggs, milk, vanilla extract, cinnamon, salt, and pepper until well combined.
Preheat a large skillet or griddle over medium heat and add 1 tablespoon of butter.
Dip each sandwich into the egg mixture, allowing it to soak for a few seconds on each side.
Place the soaked sandwiches in the skillet and cook for about 3-4 minutes on each side, or until golden brown and the cheese is melted. Add more butter as needed for cooking.
Remove from the skillet and let cool slightly. Dust with powdered sugar if desired and serve with raspberry jam on the side.