Place a tortilla on a flat work surface. On one side place a lettuce leaf and drizzle with 1 tbsp of the dressing. Layer with 1/3 cup cabbage, 2 tbsp carrot and 12 cucumber sticks. Drizzle with 1 tsp vinegar and top with some of the cilantro and mint. Roll up tightly and wrap in plastic wrap. Twist ends of wrap to secure tightly. Repeat with remaining ingredients. Refrigerate 2 to 4 hours.
To serve, unwrap rolls and cut each on the bias into 6 pieces. Serve with additional dressing for dipping, if desired.