How to Make It
Stir together 8 cups water, wine, ginger, sugar, whole scallions, and 1/2 teaspoon salt in a large Dutch oven. Remove giblets from chicken; reserve for another use, if desired. Add chicken to Dutch oven, and bring mixture to a boil over medium-high. Reduce heat to low, cover, and simmer until a meat thermometer inserted in thickest portion of thigh registers 165°F, about 1 hour and 30 minutes, skimming foam from surface of soup occasionally.
Transfer chicken to a work surface; let cool slightly. Remove and discard ginger and whole scallions from broth, and add kohlrabi and mushrooms. Cover and cook over medium-low until kohlrabi is tender, about 30 minutes.
Meanwhile, remove and discard skin from chicken; pull meat off bones. Discard bones. Shred meat into bite-size pieces.
Stir shredded chicken, bok choy, and sesame oil into soup. Cover and cook until chicken is heated through and bok choy is crisp-tender, about 10 minutes. Stir in sliced scallions and remaining 2 tablespoons salt. Ladle soup into bowls, and serve with ground Szechuan peppercorns, if using.