Heat gas or charcoal grill for direct heat. Carefully brush oil on grill rack. In large bowl, mix beef, 3/4 cup of the cooking sauce and the steak seasoning. Shape mixture into 6 patties, about 1/2 inch thick. Spray both sides of patties with cooking spray.
Place patties on grill over medium heat. Cover grill; cook 10 to 12 minutes, turning once, until meat thermometer inserted in center of patties reads 160°F. Add cheese slices during last 1 to 3 minutes of grilling or until cheese is melted.
Meanwhile, heat onion rings as directed on package. Place patties on bottom halves of buns; top each with 2 onion rings. Top with tops of buns. If desired; heat remaining sauce until hot and serve with burgers (or reserve for another use).