Makes 2 sandwiches.
Mix the marinade ingredients together. Put the pork into a shallow baking dish and pour the marinade over them. Stir to coat evenly. Chill for 1 hour.
Preheat oven to 275. Bake for 2 hours, flipping the meat once halfway through cooking.
Cut the bread in half and then cut in the long way into a top and bottom bun.
Spread the mustard evenly on all 4 pieces of bread.
Top the bottom breads with 2 slices of cheese each, then 2 pieces of the roasted pork. Next top each with 3 slices of ham, then spread the kimchi over it evenly. Top with the remaining cheese and then the top piece of bread.
Preheat a pan to medium heat and melt some butter into the pan. Add the sandwiches to the pan and top with a weight. Cover the pan to help the sandwich warm evenly.
Flip the sandwiches when they brown on the first side and cook them on the other side covered with the weight on top.
Once they are brown on both sides and heated throughout and the cheese is nice and melty, remove from heat, slice, and serve.