Place steak and 1/4 cup of the dressing in large resealable plastic bag; seal bag. Turn bag over several times to evenly coat steak with dressing. Refrigerate 30 minutes to marinate.
Preheat grill to medium heat. Remove steak from marinade; discard bag and marinade. Grill steak 5 to 10 minute on each side for medium doneness (160°F). Meanwhile, grill peppers and asparagus alongside the steak 5 to 7 minute or until crisp-tender, turning occasionally and brushing with the olive oil. Remove vegetables from grill; cut crosswise in half. Set aside. Remove steak from grill; cut across the grain into thin slices.
Place greens in large bowl. Add peppers, asparagus and remaining 1/4 cup dressing; toss to coat. Place on serving platter. Top with the steak slices; sprinkle with cheese.