Build a multi-level fire in the grill: Leave 1/4 of the bottom free of coals, bank the coals in the remaining 3/4 of the grill so that they are 3 times as high on 1 side as on the other. When the coals are all ignited and the temperature has lowered to medium (hold hand about 5-inches above grill grid, over the area where coals are deepest, for 4 to 5 seconds), the grill is ready to cook.
Make spice rub: Combine the ingredients for the spice rub in a small bowl and mix well. Rub the pork chops generously on both sides with the mixture and set aside while making the sauce.
Make the sauce: In a large skillet over medium-high heat, heat the oil until hot, but not smoking. Add the onions and cook, stirring occasionally, until golden brown, about 11 to 13 minutes. Add the peaches, ginger, and tomatoes and cook, stirring frequently for 2 minutes. Stir in the vinegar, orange juice, sugar, allspice, and salt and pepper, to taste. Bring the mixture to a boil, then reduce the heat and simmer until the mixture is reduced by about 1/2 and thickened slightly, about 20 minutes. Taste and adjust for the seasoning, then transfer the sauce to a blender or food processor and puree until smooth (be careful with hot liquids). Reserve 1/4 cup sauce for basting the chops, then pour the remaining sauce into a small serving bowl.
Put the chops on the grill over the coals and cook, turning once, until desired doneness; 8 to 10 minutes per side for medium. During the last 30 seconds of cooking on each side, baste the chops generously with the sauce. Check for doneness.
Serve the chops hot with extra barbecue sauce on the side.
Cook's note: The spice rub and barbecue sauce contains sugar, which might burn while cooking on the grill. If the chops start to burn on the outside, move them to cooler part of the grill and cover with a metal pie pan or disposable foil to finish cooking.
Recipe courtesy of Chris Schlesinger