Heat a large skillet over medium-high heat. Season both sides of pork chops with salt and pepper. Add oil and sear each side of the pork chops until golden, about 3 to 4 minutes a side. Remove and set aside.   

Add butter, onions and apples, season with salt and pepper and saute for 5 minutes. Add apple cider and hard cider and bring to a very light simmer. Add dried cherries, then nestle in pork chops and cover, making sure the liquid is at a very low simmer. Braise on the stove for 1 hour, or until the meat falls off the bone. 

Meanwhile, make the slaw. Whisk together the mayonnaise, honey, mustard, 1 tablespoon of the cider vinegar and celery seeds until smooth and season with salt and pepper. Pour the mixture over the cabbage and mix well. And more honey, if you prefer a sweeter slaw, or more vinegar, if you prefer a tangier slaw.  

Remove the pork chops from the braising liquid and set aside. Raise the heat and bring the liquid to an aggressive simmer for another 20 to 30 minutes. This will reduce and concentrate it into a beautiful onion and apple jam. Stir in the remaining tablespoon apple cider vinegar, season to taste and set aside.     

Remove bones from pork chops. To build the sandwiches, on each bottom bun, place a nice portion of the onion and apple jam, a pork chop on top of that and then some slaw. Serve with hot giardiniera.