Stir chicken, soy sauce, Sherry, and 1 tablespoon sesame oil in medium bowl to blend. Let stand 20 minutes or refrigerate up to 2 hours.
Whisk garlic, tahini, ginger, sugar, vinegar, and chili sauce in small bowl.
Heat remaining 1 tablespoon sesame oil in heavy large pot over medium-high heat. Add cabbage and green onions and sauté until cabbage is tender, about 5 minutes. Add broth and bring to boil. Add chicken with marinade and tahini-garlic mixture. Reduce heat to low and simmer until chicken is cooked through, about 5 minutes. (Can be made 1 day ahead. Cool slightly; cover and refrigerate. Bring to simmer before continuing.)
Cook noodles in large pot of boiling salted water until tender, about 5 minutes. Drain. Add to soup in pot. Stir in half of cilantro. Season soup with salt and pepper. Sprinkle with remaining cilantro.
* Sold at Middle Eastern markets, natural foods stores and some supermarkets.
** Available at Asian markets, specialty foods stores and some supermarkets.