How to Make It
Heat the oil in a large Dutch oven over medium-high. Add the chicken and cook until just opaque but not brown, about 3 minutes. Remove and set aside. Add the mushrooms, carrots, ginger, scallion whites, and miso to the pot and cook, stirring constantly, 1 minute. Add the broth and 3 cups water and bring to a boil. Reduce heat to medium-low and simmer 15 minutes.
Add the chicken to the soup and simmer 5 minutes. Add the noodles and bok choy and cook until softened, 3 to 4 minutes. Just before serving, stir in the vinegar and scallion greens.