Make brine: Lightly mash garlic with flat side of a large heavy knife. In a kettle bring water to a boil with garlic, kosher salt, peppercorns, sugar, thyme, allspice, bay leaf and simmer 15 minutes. Cool brine completely.
Working over a bowl, divide pork chops and brine among 3 large heavy sealable plastic bags and seal bags, pressing out any excess air. Marinate pork chops in bags in a large bowl, chilled, turning them once, 2 days.
Make spice rub: In a small bowl whisk together brown sugar, cumin, kosher salt and cayenne pepper.
Prepare grill. Remove pork chops from brine, discarding brine and any spices still adhering to chops, and pat dry. Season chops with salt and pepper and sprinkle both sides of each chop with about 1/2 tablespoon spice rub, patting it into meat.
Grill chops on an oiled rack set 5 to 6 inches over glowing coals, 10 to 12 minutes on each side, or until a meat thermometer diagonally inserted 2 inches into centers registers 155 degrees. (Alternatively, arrange chops in 2 lightly oiled shallow baking pans. Roast chops in upper and lower thirds of a preheated 450 degree oven, switching position of pans halfway through roasting, about 20 minutes, or until a meat thermometer registers 155 degrees.) Transfer chops to a platter and let stand 5 minutes before serving.