Combine marinade ingredients in small bowl. Place beef steak and 1/2 cup marinade in food-safe plastic bag; turn steak to coat. Close bag securely and marinate in refrigerator 6 hours or as long as overnight, turning occasionally. Cover and refrigerate remaining marinade for salad.
Spray vegetables, except tomatoes, with nonstick cooking spray.
Remove steak from marinade; discard marinade. Place steak in center of grid over medium, ash-covered coals; arrange vegetables around steak. Grill steak, covered, 12 to 14 minutes (over medium heat on preheated gas grill, 16 to 19 minutes) for medium-rare (145°F) doneness, turning occasionally. (Do not overcook.) Grill eggplant and bell peppers 12 to 15 minutes; zucchini and yellow squash 8 to 12 minutes, covered (over medium heat on preheated gas grill, eggplant 6 to 8 minutes; bell peppers, zucchini and yellow squash 7 to 11 minutes) or until tender, turning occasionally and basting with remaining reserved marinade.
Cut grilled vegetables into 1-inch pieces. Carve steak into thin slices. Toss lettuce, tomatoes and grilled vegetables with remaining 1/2 cup marinade. Divide vegetable mixture between 6 serving plates. Arrange beef steak slices over vegetables. Season with salt and pepper, as desired. Sprinkle with cheese, as desired.