Rinse the dried mushrooms. Place them in a bowl and cover with hot water, allowing them to rehydrate for an hour. Once softened, remove the mushrooms from the water and slice them. Reserve 1 cup of the mushroom-soaking water.
In a small bowl, combine vinegar and white pepper, then set it aside.
In a large pot, add the vegetable broth, ginger, and green onion. Bring it to a boil over high heat, then reduce the heat to medium. Stir in the reserved mushroom-soaking water. Reduce the heat to low and add the rehydrated mushrooms, soy sauce, and tofu.
In a separate small bowl, mix the starch with 4 tablespoons of water to create a slurry. Slowly pour the slurry into the soup while stirring to thicken it. Season with soy sauce and salt, then simmer on low heat for 10-15 minutes.
If desired, slowly pour beaten eggs into the soup while stirring.
Remove the pot from heat and stir in the vinegar and pepper mixture.
Serve the hot and sour soup garnished with fresh cilantro sprigs and a drizzle of sesame oil. Enjoy!