Soak the dried shiitake and wood ear mushrooms in hot water for 1 hour until soft.
Drain the mushrooms and squeeze out excess water, then slice into thin strips.
Bring the chicken broth to a gentle boil in a large pot.
Add the sugar, salt, light and dark soy sauces, and sesame oil to the broth.
Add the sliced mushrooms, tofu strips, and bamboo shoots to the simmering broth.
Whisk the cornstarch and cold water together to make a smooth slurry.
While stirring continuously, slowly add half the cornstarch slurry until the soup reaches desired thickness.
Create a gentle vortex in the soup with your spoon and slowly drizzle in the beaten eggs to form ribbons.
Remove from heat and stir in the white pepper and black vinegar.
Taste and adjust seasonings - add more vinegar for sourness, white pepper for heat, or salt as needed.
Ladle into bowls and top with the chopped scallions and cilantro.