Add Chinkiang vinegar and white pepper into a small bowl, mix well until the white pepper is completely dissolved.
Prepare a medium-size pot, add 1 cup marinating water from the shiitake mushrooms, 1 cup marinating water from the lily flowers, and 4 cups vegetable stock into a pot. Cook over medium-high heat. Add rehydrated wood ear mushrooms, rehydrated lily flowers, rehydrated shiitake mushrooms, tofu, bamboo shoots, ginger, light soy sauce, dark soy sauce, and salt to the pot. When the soup starts to simmer, add Napa cabbage and turn to medium-low heat. Cook until the Napa cabbage turns tender, 5 to 8 minutes.
Whisk the cornstarch with 1/4 cup of water in a small bowl until cornstarch is fully dissolved. Slowly swirl the cornstarch slurry into the soup, and stir to thicken.
Slowly swirl in the beaten egg with a fork against the edge of the bowl, and gently stir a few times to break up the eggs.
Remove the pot from stove. Add the vinegar and pepper mixture and stir to mix well. (*Footnote 6) Carefully taste the soup. Add more salt if necessary. Garnish with cilantro and drizzle with sesame oil. Stir to mix well.
Serve hot as a side or as a light main.