HEAT greased barbecue to medium-high heat. Brush steak and insides of peppers with 2 Tbsp. of the dressing.
GRILL steak and peppers 10 min. or until steak is medium doneness (160ºF), turning after 5 min. (Peppers do not need to be turned.)
MEANWHILE, place greens on four serving plates; top with tomatoes and onions. Cut steak across the grain into thin slices; cut peppers into strips. Arrange steak and peppers over salads. Drizzle evenly with the remaining 1/4 cup dressing. Sprinkle with cheese.