In a large bowl, combine the ground pork, chopped Napa cabbage, water chestnuts, green onions, ginger, soy sauce, Shaoxing wine, sesame oil, sugar, cornstarch, egg, white pepper, and salt.
Divide the mixture into four equal portions and gently shape each portion into a large, round meatball.
Add the chicken broth, water, ginger slices, green onions, soy sauce, and Shaoxing wine to a large, deep pot.
Carefully lower the meatballs into the simmering broth one at a time.
Keep the heat low enough that the broth does not boil aggressively.
Cover the pot partially and simmer for approximately 30–35 minutes.
Add the bok choy or Napa cabbage and sliced carrots during the final 8–10 minutes of cooking.
Stir in the sesame oil and season with additional salt and white pepper according to taste.
Cook until the vegetables are tender but still vibrant.
Carefully transfer one large meatball to each serving bowl.
Serve immediately with steamed rice.