To make the filling: In a large mixing bowl, add the ground pork and salt. Mix well until the pork becomes slightly sticky. Add the white pepper, sugar, soy sauce, dark soy sauce, Shaoxing wine, sesame oil, and ginger. Mix until well combined. Gradually pour in the ½ cup chicken stock, a little at a time, mixing well after each addition. Lastly, fold in the scallions until evenly distributed.
To assemble the soup dumplings: Divide the pork filling among 6 heatproof bowls. Pour the ¾ cup chicken stock among the bowls, adding enough to nearly fill each one. Place a Shanghai-style dumpling wrapper over the top of each bowl.
To steam the soup dumplings: Bring water in a large pot to a boil over high heat. Place the bowls on a steaming rack and carefully set the rack over the boiling water. Cover and steam for about 12 minutes, or until the pork is completely cooked through and reaches an internal temperature of at least 160°F (71°C). The exact cooking time will depend on how much filling you use.
To finish and serve: Carefully remove the bowls from the steamer. Top with the scallions and julienned ginger. If desired, drizzle with the chili oil, soy sauce, and Chinkiang vinegar. Serve immediately.