Broken Dumpling Soup

Name: Broken Dumpling Soup
Ingredients: 1 pound ground pork; 2 large eggs, lightly beaten; ½ cup chopped chives, divided; 1 garlic clove, finely chopped; 2 tablespoons toasted sesame oil, divided; ½ teaspoon kosher salt; ¼ teaspoon black pepper; 1 12-ounce package wonton wrappers; 10 cups low-sodium chicken broth; 2 tablespoons finely chopped, peeled fresh ginger (from a 3-inch piece); 1½ tablespoons soy sauce; 6 heads baby bok choy, stalks and leaves divided, cut into ½-inch pieces; Chili-garlic sauce, optional, for serving