Place the salt, brown sugar, peppercorns, mustard powder, and hot vinegar in a 6-quart container and stir until the salt and sugar dissolve. Let the mixture sit for 5 to 10 minutes. Add the ice cubes and stir to melt most of the ice. Add the chops, making sure they are submerged in the brine. Cover and refrigerate for 2 hours.
Heat grill to high.
Remove chops from container, rinse, and pat dry.
Place one chop at a time on its side in a bagel slicer and cut a horizontal pocket in each pork chop for stuffing. This can also be done, carefully, with a sharp knife.
Combine the cornbread, golden raisins, walnuts, dried cherries, pepper, sage, salt, and buttermilk in a mixing bowl. Place about 1/4 cup of stuffing into the pocket of each chop. Brush both sides of each chop with the vegetable oil.
Place the chops on the grill and cook for 4 minutes with the lid closed. Rotate each chop 45 degrees and cook for another 4 minutes. Flip each chop over and cook for another 4 minutes. Rotate each chop 45 degrees and cook for a final 3 to 4 minutes. Be sure to check the temperature of the chops in the thickest part of the meat, close to the bone. The chops should reach an internal temperature of 140ºF for medium. If you prefer your chops more well done, decrease the heat to low, and continue cooking until desired doneness. Remove from heat and allow to rest for at least 5 minutes before serving.