Bring a large pot of water to a boil for pasta. Once boiling, add some salt and the pasta. Cook to al dente.
Meanwhile, trim chicken and season with salt, pepper and coriander. Heat about 1 tablespoon of oil, a turn of the pan, in a large, deep skillet or wok over high heat. Add chicken and cook 4 minutes on each side. Remove to a cutting board and reserve.
Add another tablespoon of oil to the pan, a turn of the skillet, and stir-fry mushrooms a few minutes to soften and brown. Stir in ginger and garlic, toss a minute or two more then add vinegar. Stir, add Tamari and stock, and bring to a boil.
Thinly slice the chicken on an angle into strips. Add chicken to soup. Combine cornstarch and water in a small bowl and stir into broth. Let thicken a minute more. Add scallions and bean sprouts to soup and turn off heat.
Twist a bundle of noodles up around tongs or a serving fork and pile into individual bowls. Ladle soup over the noodles and garnish with cilantro and lime juice. Pass hot sauce at the table.