Mushrooms and bok choy are full of antioxidants. Along with scallions, dill, ginger, and chiles, they give this soup its nuanced taste.
Combine chicken stock, water, ginger, scallions, chile, dill, and reserved mushroom stems in a medium pot over medium heat. Bring to a low simmer. Add chicken, and cook until an instant-read thermometer inserted into the thickest part of the meat reaches 160 degrees, 13 to 15 minutes.
Remove chicken, and cover. Strain broth through a fine sieve; discard solids. Return broth to pot, and bring to a simmer. Add sliced mushroom caps and bok choy, and simmer until tender, about 5 minutes.
Slice chicken, and divide among 4 bowls. Ladle broth, with vegetables, over chicken, and garnish with scallions and chile.