1Brush grill rack with vegetable oil. Heat coals or gas grill for direct heat.
2Mix all ingredients except onion, bread and oil. Shape mixture into 4 patties, about 3/4 inch thick.
3Cover and grill patties 4 to 5 inches from medium heat 15 to 18 minutes, turning once, until no longer pink in center. Add onion slices to grill for last 8 to 10 minutes of grilling, turning once, until golden brown. Brush both sides of bread slices with oil. Add bread to grill for last 2 to 3 minutes of grilling, turning once, until golden brown.
4Serve burgers and onion between bread slices.