Lay out 4 bottom slices of bread. If using Dijon, spread about 1/2 tbs Dijon per slice. Top each with 2 slices ham, 2 slices turkey, and 2 slices Swiss cheese. Close with remaining 4 slices of bread to form 4 sandwiches. Press gently to compress layers for an even cook.

Trim crusts if preferred and cut each sandwich in half diagonally or keep whole.

Batter & Coating

Make egg batter

In a shallow dish large enough to dunk each sandwich, whisk together eggs, milk, flour, salt, and pepper until smooth and slightly frothy. The batter should be pourable but coat the bread — adjust with a teaspoon of milk or flour if needed.

Heat pan

Heat a large skillet over medium to medium-low heat. Add the butter and the optional teaspoon of neutral oil (helps prevent burning). Once butter is melted and foaming but not browned, reduce heat to medium-low to allow gentle browning without burning.

Coat and cook sandwiches

Working with one sandwich at a time, dip the top and bottom quickly into the egg batter so the bread soaks but doesn’t fall apart (about 3–5 seconds per side). Let excess drip off. Place the dipped sandwich in the skillet. Cook 3–4 minutes per side, pressing gently with a spatula, until golden brown and cheese is melted. If the outside browns too quickly before the cheese melts, lower heat and cover skillet for 1–2 minutes to help cheese melt through.

If cooking multiple sandwiches, add more butter as needed and warm finished sandwiches in a low oven (100–120°C / 210–250°F) on a rack while you finish the rest to keep crispness.

To Serve

Transfer sandwiches to a cutting board. Dust tops lightly with powdered sugar. Serve immediately with a small bowl of jam on the side for dipping and pickle spears if desired.

Makes 4 sandwiches (8 halves).