In large bowl, combine ground beef, salt, pepper and onion; mix thoroughly. Shape into 12 quarter-inch-thick patties. Reserve 1/3 cup shredded pepper jack. Top six patties with remaining cheese.
Place remaining patties over cheese-topped patties and firmly press edges together. Spray grate of outdoor grill and utensils with PAM For Grilling Spray. Heat grill to medium.
Place burgers on grill and cook, covered, 7-8 minutes to medium doneness, until no longer pink in center and juices show no pink color; turning occasionally. During last 2 minutes of cooking, spoon 1 tablespoon of salsa on each burger and sprinkle with remaining cheese. Serve immediately.