Heat oven to 400° F.
Spread the mustard on 6 pieces of the French toast. Divide the ham and turkey evenly among them and top each with 2 slices of the cheese.
Spread the remaining 6 pieces of French toast with the mayonnaise (if desired) and sandwich together.
Heat a large skillet over medium heat. Spread ½ tablespoon of the butter on the top and bottom of each sandwich.
Cook 3 sandwiches in the skillet until brown, 2 minutes per side. Transfer to a baking sheet. Repeat with the remaining sandwiches.
Transfer to oven and bake until the cheese is melted and the toast is heated through, about 4 minutes.