Drunken Chicken Soup

Name: Drunken Chicken Soup
Ingredients: 8 cups water; 1 (750-ml) bottle Shaoxing wine or dry sherry (not cooking wine); 4 ounces fresh ginger, peeled and sliced (about 3/4 cup) (from 1 [7 1/2-inch] piece); 3 tablespoons granulated sugar; 6 whole scallions; 2 tablespoons plus 1/2 teaspoon kosher salt, divided; 1 (3 1/2-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)