1Heat gas or charcoal grill. In medium bowl, mix all patty melt ingredients except bread and cheese. Shape mixture into 4 patties, about 3/4 inch thick. Refrigerate while cooking onions.
2In 8-inch skillet, heat oil over medium-high heat. Cook onions in oil, stirring frequently, until tender. Stir in salt and pepper; keep warm.
3Place patties on grill rack over medium heat. Cover grill; cook 12 to 15 minutes, turning once, until meat thermometer inserted in center of patties reads 160ºF. Add bread slices to side of grill for last 5 minutes of grilling, turning once, until lightly toasted. Top patties with cheese. Cover grill; cook about 1 minute longer or until cheese is melted. Place patties on bread; top with onions.