Preheat a waffle iron according to manufacturer's instructions.
Mix mayonnaise and Dijon mustard together in a bowl; spread onto 1 side of each bread slice. Sprinkle pepperjack cheese over mayo-mustard layer of 2 bread slices. Cover cheese layer with a second bread slice, creating 2 whole sandwiches.
Place 1 sandwich in the waffle iron, taking care not to push down all the way. Wait until the bread begins to soften from the heat before starting to gently close the waffle iron, about 2 minutes. Apply more pressure to the top part of the iron, eventually closing it after a total of 3 to 4 minutes. Cook until browned, 2 to 3 minutes more. Repeat with the remaining sandwich.