In a large nonstick skillet over low heat, cook onions in butter and oil for 1 hour or until tender, stirring occasionally. Sprinkle with sugar, salt and pepper; cook over medium low heat for 45-60 minutes or until golden brown, stirring occasionally. In a large bowl, combine the green onions, Worcestershire sauce and pepper sauce; crumble turkey over mixture and mix well.
Shape into six patties. Coat grill rack with nonstick cooking spray before starting the grill. Grill burgers, covered, over medium hot heat for 5-7 minutes on each side or until a meat thermometer reads 165 degrees F and juices run clear. Serve on buns with caramelized onions.