HEAT oil in large nonstick skillet on medium-high heat. Add onions; cook 8 min. or until golden brown, stirring frequently and adding barbecue sauce the last few minutes. Remove onions from skillet; set aside. Carefully wipe skillet clean with paper towel.
SHAPE meat into 4 (1/2-inch-thick) patties. Add to skillet; cook on medium heat 4 to 5 min. on each side or until done (160ºF). Top with Singles; cook 1 min. or until melted.
FILL toast slices with burgers and onions to make 4 sandwiches.