Start by making a marinade for the pork: Combine the orange juice, lime juice, olive oil, cilantro, garlic, oregano, cumin, and orange zest in a large zip-top bag. Use a meat mallet to pound the pork chops as thinly as possible. Season the pork chops directly with kosher salt and add them to the marinade. Marinade the chops for at least 4 hours or overnight.
Remove the pork chops from the marinade and use the leftover marinade to make a glaze. Bring the marinade to a boil and add the sugar, honey, mustard, and cider vinegar. Reduce the mixture by half, this will take about 10 minutes.
Heat a griddle or grill to medium high heat. Cook the pork chops directly on the grill for 1 to 2 minutes per side. Brush the pork chops with the glaze and continue to flip and glaze for 2 to 3 minutes. The pork chops should reach at least 145 degrees F, have some golden brown color but still be juicy. Remove the chop from the griddle and cool for 5 minutes before thinly slicing.
Build the sandwich by spreading an even layer of mustard on one side of the bread. Layer on the Kaylin + Kaylin pickles, the sliced pork, ham, and cheese. Add the top half of the bread, butter it and return the whole sandwich to the grill butter side down. Press the sandwich with weights or a large heavy skillet and cook for 5 minutes or until the bread is crispy. Slice the sandwich and serve.