Lightly toast the waffles until just crisp and warm; set aside.
In a shallow dish, whisk together the eggs, milk, vanilla, salt, and pepper to make the custard.
Assemble 4 sandwiches: Spread Dijon on 4 waffles and raspberry jam on the remaining 4. Layer turkey, ham, and Swiss cheese on the Dijon sides, then top with the jam waffles.
Working one at a time, press each sandwich gently to compact, then dip both sides into the egg mixture until coated but not saturated.
Heat a large nonstick skillet over medium heat and add the butter. Cook sandwiches 3 to 4 minutes per side, until deep golden and the cheese is melted. Keep warm in a 200°F oven if needed while you cook the rest.
Dust with powdered sugar and serve warm with maple syrup.
Notes
Swap Swiss with Gruyère or provolone, and try strawberry or blackberry jam. For extra crisp edges, press the dipped sandwiches in a waffle iron lightly greased with butter.