With about 15-30 minutes remaining on the soup, start making the noodles.
Heavily flour a cutting board and a clean, dry plate.
Roll small chunks of dough into thin, rectangular sheets. Flour to keep from sticking. Cut into thin noodles strips with a knife or cleaver (1/4 to 1/8 inch thick).
Place onto the plate, sprinkle with flour, and mix by hand—keep them well floured to prevent them from sticking together.
Bring large pot of water to boil.
Place the cut dough noodles into boiling water, bring to boil, reduce heat, and boil for at least 5 minutes.
Pour into strainer and rinse with cold water.
Put noodles into bowls. Spoon in chicken pieces. Pour soup onto the chicken and noodles through a strainer. Sprinkle with sesame oil and garnish with cut green onions.