In medium heatproof bowl, dissolve salt and sugar in boiling water, stir in ice cubes to cool. Add the pork chops, cover bowl with plastic wrap, and refrigerate to marinate, about 30 minutes. Remove from brine, rinse well, and dry thoroughly with paper towels.
Heat a medium sauté pan over medium heat. Spray with nonstick spray. Add the onion and cook until translucent, about 2 minutes. Add the garlic and ginger and cook until fragrant, about 45 to 60 seconds.
Add the ketchup, peach jam, and peaches. Reduce heat to low and simmer until sauce thickens, about 30 minutes, stirring occasionally. Add vinegar, season with salt and pepper. Remove from heat, set aside to cool.
Pour half the barbecue sauce into a shallow baking dish, reserve remaining sauce. Add pork chops, turning to coat both sides.
Prepare a medium-hot grill or grill pan. Grill chops until cooked through, about 5 minutes per side, basting chops with barbecue sauce. Remove from grill, let stand 5 minutes before serving. Serve with the remaining sauce.