HEAT greased grill to medium heat.
SHAPE turkey into 5 patties. Grill patties and onions 8 to 10 min. or until burgers are done (165ºF) and onions are tender, turning after 5 min. Top burgers with cheese.
REMOVE burgers and onions from grill. Place onions in bowl. Add barbecue sauce; toss to coat.
FILL buns with arugula, cheeseburgers and onions.