Whisk barbeque sauce, apple butter, brown sugar, black pepper, and garlic together in a microwave-safe bowl; heat in microwave until sugar dissolves, about 30 seconds. Stir until sauce is smooth.
Place pork chops on a plate and pour sauce over chops. Refrigerate for flavors to soak into pork chops, 1 to 2 hours.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Cook pork chops on grill until cooked through, about 15 minutes. An instant-read thermometer inserted into the center should read 145 degrees F (63 degrees C).