Spread 4 bread slices with Dijon and layer each with Swiss, ham, turkey, another Swiss slice and a second piece of bread.
Press the sandwiches gently and trim only any loose meat that extends beyond the bread.
Whisk the eggs, milk and salt in a shallow dish until no streaks remain.
Melt half the butter on a griddle over medium-low heat, dip 2 sandwiches quickly on both sides and place them on the griddle.
Cook for 3 to 4 minutes per side until golden, the egg coating is set and the center reaches 165°F; repeat with the remaining butter and sandwiches.
Dust each sandwich with 1/2 teaspoon powdered sugar, cut diagonally and serve hot.
