Combine the pork, eggs, ¼ cup of the chives, garlic, and ¼ teaspoon of the sesame oil in a medium bowl with the salt and pepper. Form into 30 tablespoon-size balls; chill for 15 minutes.
Meanwhile, slice the wonton wrappers into ½-inch noodles. Bring a medium pot of salted water to a boil. Cook the wonton noodles for 1 minute, stirring to keep from sticking. Drain and rinse; reserve in a bowl of cold water.
Combine the broth, ginger, soy sauce, and remaining sesame oil in a large pot. Simmer 15 minutes. Add the meatballs; cook until just firm, 7 minutes more. Add the bok choy stalks and cook 3 minutes more. Add the bok choy leaves and remaining chives.
Stir in the wonton noodles to warm and serve with chili-garlic sauce, if desired.