Combine 3 tablespoons rice vinegar and remaining marinade ingredients in small bowl. Reserve 1/4 cup marinade mixture for serving. Place beef steak and remaining 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.
Meanwhile, combine cucumbers, carrots and 1/2 cup rice vinegar in medium bowl. Cover and refrigerate until ready to use.
Remove steak from marinade; discard marinade. Place steak on grid over medium, ash-covered coals; Grill, covered, 11 to 16 minutes (over medium heat on preheated gas grill, 16 to 21 minutes) for medium rare (145°F) to medium (160°F) doneness, turning occasionally.
Drain vegetable mixture; discard liquid. Carve steak lengthwise in half, then crosswise into thin slices. Top tortillas evenly with steak slices and vegetables. Drizzle with reserved marinade and sprinkle with green onions, if desired.
Nutrition information per serving, using flank steak: 159 Calories; 36 Calories from fat; 4g Total Fat (1 g Saturated Fat; 1 g Monounsaturated Fat;) 33 mg Cholesterol; 205 mg Sodium; 17 g Total Carbohydrate; 1.8 g Dietary Fiber; 14 g Protein; 1.2 mg Iron; 5.5 mg NE Niacin; 0.3 mg Vitamin B6; 0.7 mcg Vitamin B12; 2.5 mg Zinc; 13.8 mcg Selenium; 47.3 mg Choline.
This recipe is an excellent source of Protein, Niacin, Vitamin B12, Zinc, and Selenium; and a good source of Vitamin B6.