Cook egg noodles in one litre of boiling water until al dente, about three minutes. Drain and toss with a small amount of toasted sesame oil to prevent sticking; set aside.
Have stock heating in a pot.
Heat a large wok over high heat. When wok begins to smoke, add peanut oil. Stir-fry ginger and chile for less than 30 seconds. Add chicken and let settle for one minute before stir-frying. As chicken begins to brown, add rice wine and stir-fry until wine has almost evaporated. Carefully stir in the tofu then add in the mushrooms, bamboo shoots, and the white parts of the napa cabbage and stir-fry for one minute. Add the hot stock. Bring to a boil then reduce to simmer. Season the soup with soy sauce, black rice vinegar, salt, and freshly ground white pepper. Stir in green parts of the Napa cabbage and continue to simmer for 10 minutes, skimming off any foam that arises.Divide noodles into four bowls. Ladle some of the soup over the noodles and garnish with scallions and cilantro.