In the bowl of a food processor fitted with the metal blade, puree the peaches and tomatoes until smooth; set aside.
Heat the oil in a medium saucepan over medium-high heat until shimmering. Add the onion and cook, stirring occasionally, until golden brown, 5 to 7 minutes.
Add the ginger and cook, stirring frequently, until fragrant, 1 to 2 minutes.
Add the reserved peach-tomato puree, vinegar, honey and bourbon; season with salt and pepper, to taste. Bring the mixture to a boil over high heat, then decrease the heat to simmer.
Cook until the mixture is reduced by half and thickened, about 20 minutes. Taste and adjust for the seasoning with salt and pepper.
Reserve ¼ cup sauce for basting the chops, and keep the remaining sauce warm in the saucepan until ready to serve.
Meanwhile, place the remaining ¼ cup salt and brown sugar in a medium heatproof bowl.
Pour the 2 cups boiling water over the mixture and stir to dissolve. Add the ice cubes and stir to cool.
Add the pork chops, cover the bowl with plastic wrap, and refrigerate to marinate, about 30 minutes. (Do not marinate any longer or the pork will be too salty. If you can’t cook it right at the 30-minute mark, remove the pork from the marinade and refrigerate until ready to continue.)
Remove from the brine, rinse well, and thoroughly dry pat with paper towels. Set aside.
Season the pork chops with pepper.
Prepare a charcoal fire using about 6 pounds of charcoal and burn until the coals are completely covered with a thin coating of light gray ash, 20 to 30 minutes.
Spread the coals evenly over the grill bottom, position the grill rack above the coals, and heat until medium-hot (when you can hold your hand 5 inches above the grill surface for no longer than 3 or 4 seconds). Or, for a gas grill, turn all burners to high, close the lid, and heat until very hot, 10 to 15 minutes. Or, preheat a grill pan over medium-high heat until hot.
Place the pork chops in the grill pan or on the grill and grill for 3 to 5 minutes per side or until the internal temperature reaches 145°, brushing with Peach Barbecue Sauce in the last few minutes.
Remove to a plate and cover with aluminum foil to rest and let the juices redistribute, 3 to 5 minutes.
Serve immediately with reserved warm sauce on the side.