Spread mustard on bread. Layer 4 bread slices with Swiss cheese, ham, and cheese again. Place remaining bread slices on top.
In a shallow dish, whisk together eggs, milk, salt, pepper, and nutmeg. Dip each sandwich in the egg mixture, turning to coat well.
In a large skillet, melt butter over medium-low heat. When butter is foamy, add the sandwiches, and cook, turning once, until golden brown on both sides, 6 to 8 minutes total. Serve immediately, dusted with confectioners' sugar.