Heat a heavy pan over medium-low heat.
On all four slices of bread, spread the softened butter on one side and dijon mustard on the other. Place two slices of the bread, butter-side-down in the pan. Top with the grated cheese and another slice of bread, butter side up. Press down gently on the sandwiches. Once the cheese has started to melt and you have a nice color on the base, flip the sandwich over and continue to cook until the cheese has fully melted and the bread is golden (about 4 minutes on each side).
Slice each sandwich 3×3 (9 pieces total) and spear two pieces together with a toothpick to serve. Don’t forget the ketchup for dipping!