Makes 1 sandwich.

1. On a work surface, lay out 2 slices of bread and spread with mayonnaise. Top each slice with the 1 slice of swiss and 1 slice of turkey each. Put the third slice of bread on top of one stack, and flip the remaining stack on top, cheese-side down, to make a triple-decker sandwich.
2. Using a knife, cut the crusts off the sandwich (this helps to pinch and seal the ends). Wrap the sandwich tightly with plastic wrap and refrigerate for at least 30 minutes and up to 6 hours. (Wrapping the sandwich in plastic wrap compacts it and prevents the egg batter from seeping in.)
3. Combine the eggs and milk in a bowl. Heat the oil and butter in a skillet over medium-high heat. Unwrap the sandwich and dip it in the egg batter, to coat evenly. Gently place it in the skillet, and fry, turning once, until golden brown and hot, about 5 minutes total.
4. Cut the Monte Cristo in half, transfer it to a plate, dust with powdered sugar, and spoon some jam over each half. Serve immediately.