In a wide, shallow bowl, beat eggs and milk to combine.
Lay out 4 Eggo Waffles on a work surface and top each with 2 slices turkey, 1 slice cheese, 2 slices ham. Then top each with one of the remaining 4 Eggo Waffles.
Warm a large nonstick frying pan over medium heat. Melt butter (if pan is not large enough to accommodate all 4 sandwiches, melt half of butter and cook sandwiches in 2 batches). When butter sizzles, swirl pan to coat.
Carefully dip each sandwich in egg mixture, turning to lightly coat both sides. Shake off excess egg mixture.
Lay sandwiches in hot pan. Cook, turning once, until sandwiches are well-browned on both sides.
To serve, cut sandwiches in half and sprinkle lightly with powdered sugar, if desired. Serve jam alongside sandwiches for dipping. Serves 4.