Cook the noodles al dente, as they will be boiled again, and set aside.
Combine breast and wings in large pot and cover with water, bring to boil and then toss in several scallions and an inch of sliced ginger, 1 tsp salt, medium low, covered, until chicken is cooked through. Skim the water as chicken cooks to remove the foamy white film
Remove chicken into a bowl and strain broth and reserve
Let chicken cool and then pull breasts into small peices. Adding the wing meat is optional, it mostly provides broth,but I usually add a least some of it.
Heat oil in large pot. Add chopped garlic, chopped ginger (inch or so), mushrooms and more salt. Lightly saute for a couple minutes.
Wash bok choy off, cut into large pieces with stems cut in bite-sized. Add to pot and cook until wilted, not too long, 5 minutes or so.
Add back the broth, the chicken, soy sauce and vinegar, bring to boil, reduce heat and simmer for 5 minutes.
Add salt as needed, serve in bowl with yoru choice of noodles and chopped scallions.