To season the seafood, in a bowl, combine the shrimp and scallops with the salt and white pepper. Mix gently and set aside.
To prepare the seasonings, in a small bowl, combine the soy sauce and salt. In another bowl, combine the Chinkiang vinegar, white pepper, dark soy sauce, and sesame oil.
To cook the soup, in a large pot over high heat, bring the chicken stock to a boil. Add the first seasoning and stir to combine. Add the shiitake mushrooms, wood ear mushrooms, bamboo shoots, carrot, and ginger. Boil for about 4 minutes until softened.
To add the seafood, add the tofu, shrimp, and scallops. Boil for about 1 minute until the seafood is nearly cooked through.
To thicken the soup, in a small bowl, combine the cornstarch and water. Stir until smooth, then slowly pour the slurry into the soup while stirring. Cook until lightly thickened.
To finish the soup, add the second seasoning and bring the soup back to a boil. Slowly drizzle in the beaten eggs in a circular motion. Let the eggs set for a few seconds, then gently stir. Garnish with the scallions and serve hot.