Prepare the mushrooms: Place dried Shiitake and wood ear mushrooms in separate bowls and soak them in 1 cup of water until soft. If you are using fresh Shiitake mushrooms, skip this step.
Once the mushrooms are soft, squeeze out the water. Keep the mushrooms water for later. Cut the mushrooms into thin strips. For wood ear mushrooms, remove the tough ends before slicing.
Next, heat a 5-quart pan and add a tablespoon of oil. Sauté mushrooms and carrots until the mushrooms release their aroma. Add the wood ear mushrooms and bamboo shoot, then stir-fry for a few seconds over medium-low heat.
Swirl in the soy sauce around the side of the pan and quickly stir the mixture to combine. Mix the mushrooms water in water to make 6 cups of liquid, then add to the pot.
Season with ground pepper, Shao Xing wine, sugar, and mushroom seasoning. Give the mixture a quick stir and add the mung bean thread and tofu.
Bring the mixture to a boil and cook for another minute or so. Taste and season if needed.
Now, mix 2 tablespoons of cornstarch in 3 tablespoons of water until well combined. Add this thick slurry into the soup while stirring continuously. The soup should start to thicken by now. If not, add more cornstarch slurry.
Turn off the heat and ladle the soup into a large bowl.
Swirl in the vinegar and add a splash of chile and toasted sesame oil. Finally, garnish with fried wonton strips and chopped cilantro. Serve warm.