Place 1 cup of the salt, the brown sugar, peppercorns, mustard and 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 and make sure they are submerged in the brine. Cover and refrigerate 25 minutes.
Preheat the oven to 500 degrees F with the oven rack in the center of the oven.
Remove the chops from the brine, rinse and pat dry. Holding a knife parallel to the cutting board, cut a deep 2-inch-wide pocket into the side of each pork chop.
Combine the cornbread, walnuts, dried cherries, raisins, pepper, sage, 2 teaspoons salt and the buttermilk in a mixing bowl. Place about 1/4 cup of the stuffing into the pocket of each chop. Brush both sides of each chop with the oil.
Heat a cast-iron skillet until smoking hot, about 600 degrees F. Add the chops to the pan and cook until well seared, about 5 minutes per side.
Transfer the pan to the oven and cook about 12 minutes more or until the internal temperature of the chops reaches 140 degrees F for medium. Be sure to temp the chops in the thickest part of the meat close to the bone, not in the stuffing. Let the chops rest 5 minutes before serving.