FOR DRESSING: Combine all dressing ingredients in small saucepan and simmer for 3 minutes. Set aside to cool.
FOR SALAD: Soak noodles in warm water for 20 minutes. Drain and cut into 4-inch lengths.
TO SERVE: Mix together noodles, carrots, pickles, and cucumber in small salad bowl. Pour on dressing and toss to combine. Chill and serve.