8 cups Water
1 (750-ml) bottle Shaoxing Wine or Dry Sherry, (not cooking wine)
4 ounces fresh Ginger, peeled and sliced (about ¾ cup) (from 1 [7 ½-inch] piece)
3 tablespoons Granulated Sugar
6 whole Scallions
2 tablespoons plus ½ teaspoon Kosher Salt, divided
1 (3 ½-pound) Whole Chicken
1 pound Kohlrabi, peeled and cut into 1-inch pieces
4 ounces Shiitake Mushrooms, stemmed and cut into 1-inch pieces (about 2 cups)
3 Baby Bok Choy, trimmed and sliced (about 4 cups)
2 tablespoons Toasted Sesame Oil
1 cup thinly sliced Scallions
Ground Szechuan Peppercorns, for serving (optional)
Stir together 8 cups water, wine, ginger, sugar, whole scallions, and ½ 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.