Cook noodles according to package directions, omitting salt and fat. Drain; rinse with cold water.
Combine noodles, shredded cabbage, carrot, 1/2 cup green onions, and shrimp in a large bowl.
Combine soy sauce and next 4 ingredients (through chile paste) in a small bowl; stir with a whisk until blended. Add soy sauce mixture to noodle mixture, tossing gently to coat. Sprinkle with remaining 1/4 cup green onions and peanuts.