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.
Heat oven to 500ºF with the oven rack in the center of the oven.
After 25 minutes, 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 large mixing bowl. Place about 1/4 cup of the stuffing into the pocket of each chop. Brush both sides of each chop with oil.
Heat a 12-inch cast-iron skillet until smoking hot, about 600ºF. Add the chops to the pan and cook until well seared, about 5 minutes per side.
Transfer the pan to the oven and cook until the internal temperature of the chops reaches 140ºF for medium, about 12 minutes. Be sure to check the temperature of 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.