Combine Rub ingredients. Press 2 tablespoons evenly onto beef steak; set aside. Brush vegetables with oil and sprinkle evenly with remaining rub.
Place steak in center of grid over medium, ash-covered coals; arrange eggplant and onion around steak. Grill steak, covered, 11 to 15 minutes (over medium heat on preheated gas grill, 13 to 16 minutes) for medium rare (145°F) to medium (160°F) doneness, turning occasionally. Grill eggplant 6 to 8 minutes; onions 12 to 15 minutes (gas grill times remain the same) or until tender, turning occasionally.
Cut vegetables into bite-size pieces. Carve steak into slices; then cut slices crosswise in half. Arrange beef and vegetables on serving plates. Season with salt and pepper, as desired. Evenly divide beef and vegetables among flatbreads; garnish with Toppings, as desired.
Nutrition information per serving: 462 Calories; 135 kcal Calories from fat; 15 g Total Fat; 3 g Saturated Fat; 7 g Monounsaturated Fat; 70 mg Cholesterol; 387 mg Sodium; 46 g Total Carbohydrate; 7.6 g Dietary Fiber; 34 g Protein; 4.2 mg Iron; 15.3 mg Niacin; 0.7 mg Vitamin B6; 1.5 mcg Vitamin B12; 5.7 mg Zinc; 47.3 mcg Selenium; 118.9 mg Choline;