In a large bowl, stir together the water, sea salt and sugar. Add pork chops to this brine, and let them soak for no more than one hour. Drain and discard the brine. Pat pork chops dry with kitchen paper.
In a shallow dish, stir together the olive oil, garlic and rosemary. Place pork chops in the dish and turn to coat. Cover and marinate in the refrigerator for at least 1 or 2 hours.
Pour the balsamic vinegar into a small saucepan. Bring to the boil, and cook until reduced by 1/2, about 10 minutes. When the vinegar cools, it should be the consistency of syrup.
Melt butter with olive oil in a large frying pan over medium-high or high heat. Add the onions and pears, and quickly brown being careful to keep the wedges intact. Once the onions and pears are browned, reduce heat to low, and cook for about 7 minutes, or until tender. Stir in the reduced vinegar and salt. The recipe can be prepared up to this point several hours before barbecuing.
Preheat the barbecue for medium-high heat.
Warm pears on a cool section of the barbecue (in the frying pan), while placing the pork chops over the hot part. Cook pork for about 3 minutes per side, or to desired doneness. Remove to a serving plate, cover with aluminium foil and let rest for a few minutes. Uncover, top with the pear onion sauce and serve.