1To brine pork chops: Bring vinegar, brown sugar, salt, mustard, and peppercorns to a simmer over medium heat, stirring to dissolve salt. Do not inhale fumes. Transfer to large, deep food-safe container. Let cool until tepid. Stir in iced water. Submerge chops in brine. Refrigerate for 3 hours, no longer.
2To make stuffing: Melt butter in a large skillet over medium heat. Add chorizo and cook, stirring occasionally, until lightly browned, about 5 minutes. Add celery, dates, and shallot, and cook, stirring often, until celery is tender, about 5 minutes. Stir in parsley, sage, and paprika. Transfer to a bowl and let cool completely. Stir in cheese and season with salt and pepper.
3Remove chops from brine, rinse under cold water, and blot dry with paper towels. Cut a horizontal pocket in each chop to the bone using a sharp knife. Spoon equal amounts of stuffing into each chop, and close each opening shut with wooden toothpicks. Do not overstuff the chops; you may not use all of the filling.
4Prepare a medium fire in an outdoor grill. (For a gas grill, preheat to about 400ºF. For a charcoal grill, let the coals burn until covered with white ash and you can hold your hand about an inch above the cooking grate for 3 seconds.) Brush cooking grates clean. Grill pork, with the lid closed as much as possible, turning occasionally, until an instant-read thermometer inserted horizontally into the center of a chop reads 145ºF, about 15 minutes. Remove from the grill and let stand for 3 to 5 minutes.
5Remove toothpicks and serve.