Heat gas or charcoal grill. Sprinkle beef steaks with 3 teaspoons of the grill seasoning. In large bowl, mix bell peppers and onion with oil and remaining 1 teaspoon grill seasoning. Spoon vegetables into grill basket (grill “wok”).
Place steaks and grill basket on grill over medium heat. Cover grill; cook 8 to 10 minutes, turning steaks once and stirring vegetables 2 or 3 times, until beef is desired doneness and vegetables are crisp-tender. Place cheese on steaks. Cover grill; cook about 1 minute longer or until cheese is melted.
Place each steak on serving plate. Spoon vegetables over steaks.