Pour the chicken stock into a medium size pot. Add onion, scallion, garlic, and ginger. Bring it to a boil over medium high heat. Add the chicken breast, and when it comes to a boil again, reduce the heat to medium low. Cover, and continue to boil.
Turn the heat off and remove the chicken to a bowl. Place the pot in an ice bath to cool. Strain the stock, and discard the aromatic vegetables. Stir in all the seasoning ingredients, and keep it in the freezer to chill, preferably until it becomes slushy.
When the chicken is cool enough to handle, shred and lightly season with salt, pepper, sesame oil, and minced garlic. Refrigerate while preparing the vegetables.
Thinly slice the red cabbage and red bell pepper. If serving with the noodles, cook the noodles according to the package instructions. Be sure to rinse them in icy cold water, and drain.