1. Prepare Onion Jam: Sauté onions in hot oil in a large nonstick skillet over medium-high heat 10 minutes. Reduce heat to low; stir in sugar, vinegar, and thyme. Cover and cook 10 minutes or until onion is very tender. Keep warm.
2. Prepare Burgers: Coat cold cooking grate of grill with vegetable cooking spray, and place on grill. Preheat grill to 350° to 400° (medium-high) heat. Gently stir together ground round and next 3 ingredients. Shape mixture into 4 (1/2-inch-thick) patties.
3. Grill patties, covered with grill lid, 5 minutes on each side. Top with preserves and cheese; grill 2 minutes or until beef is no longer pink in center and cheese is melted. Serve burgers on buns with desired amount of Red Onion Jam.