How to Make It
In a stockpot, combine the chicken and neck with the water, onion, carrots, celery, garlic, peppercorns, bay leaf, parsley springs and thyme sprigs and bring to a boil. Cover partially and simmer over low heat for 30 minutes. Transfer the chicken to a plate. Discard the skin. Pull the meat off the bones, cut it into 1/2-inch pieces and refrigerate.
Return the bones to the pot, partially cover and simmer for 1 hour, until the broth is richly flavored. Strain the broth into a clean heat proof bowl and rinse out the pot. Return the broth to the pot and boil over moderate heat until reduced to 8 cups, about 30 minutes. Season with salt.
In a medium saucepan of boiling salted water, cook the udon until al dente. Drain and cool under running water. Drain again.
In a large skillet, heat the vegetable oil. Add the mushrooms and cook over high heat, stirring, until golden, about 7 minutes. Scrape the mushrooms into the stockpot and add the udon, ginger, tofu, kimchi, fish sauce and sesame oil. Season with salt and simmer for 5 minutes. Add the chicken and simmer until just heated through. Ladle into bowls and serve.