Combine first 8 ingredients in a large bowl; stir with a whisk until blended.
Cook peas in boiling water 1 minute or just until crisp-tender. Drain and rinse with cold water; drain well.
Cook noodles according to package directions; drain and rinse under cold water. Drain well. Add noodles, peas, chicken, cilantro, and parsley to soy sauce mixture; toss well.