Prepare a grill for indirect heat: For gas, preheat to medium high, then turn off the burners on one side and turn the other burners to medium low. For charcoal, once the coals ash over, push them to one side.
Whisk 1/4 cup salt, 1/4 cup brown sugar and 3 cups warm water in a large bowl. Add the pork and soak 10 minutes. Meanwhile, mix the bourbon, vinegar, Worcestershire sauce, the remaining 1/4 cup brown sugar, the garlic and ginger in an ovenproof saucepan. Put on the grill over direct heat; bring to a boil, then remove from the grill.
Grill the onion and tomatoes over direct heat until charred, about 3 minutes per side for the tomato and 4 to 5 minutes per side for the onion. Add to the saucepan, then return the pan to the grill and cook until the sauce is thickened, about 15 more minutes.
Remove the chops from the brine; pat dry. Brush with the vegetable oil and grill over direct heat, 2 to 3 minutes per side. Transfer to the cooler side of the grill and cook 3 to 4 more minutes per side, brushing with the sauce. Serve with the remaining sauce and vegetables.