Hear a large pot over medium-high heat. Add butter; swirl to coat. Add half each of the chicken and ginger and sauté for 2 minutes or until chicken is no longer pink inside, transfer to a bowl (some ginger will stick to pot). Repeat with remaining chicken and ginger. Set aside.
Add broth, soy sauce, vinegar and chili sauce to pot; increase heat to high and bring to boil scraping up brown bits. Stir into mushrooms, celery and noodles.
Whisk cornstarch into milk; stir into pot.
Reduce heat to medium and cook, stirring, for 5-10 minutes or until bubbling and noodles are tender.
Stir in chicken mixture. Season to taste with chili sauce.
Using tongs, divide chicken and noodles among warmed serving bowls; ladle broth on top.
Garnish with red pepper and green onions.
FOR THE ADVENTUROUS: For Korean flair, add 1 tablespoons fish sauce and 1/2 teaspoons hot pepper flakes with broth and garnish each bowl with kimchi.