In a small bowl, stir together the black vinegar, light soy sauce, white pepper, and sugar. Add more white pepper (spice) and/or black vinegar (sour), if desired.
In a large pot, combine the mushrooms, carrots, bamboo shoots and vegetable stock. Bring to a simmer over medium heat and cook for 3 to 4 minutes, until the carrots start to soften. Gently add the tofu and cook for another 2 to 3 minutes, until the tofu is slightly browned. Pour in the sauce and simmer for 1 to 2 minutes, until fragrant.
Meanwhile, in a small measuring cup, stir together the cornstarch and water until smooth.
Pour the cornstarch mixture into the pot. Stir well to ensure the cornstarch does not settle at the bottom of the pot. Simmer for 1 minute, or until the soup is thicker. Remove from the heat.
Using a ladle, stir the soup in one direction. While stirring, slowly drizzle in the beaten eggs from 8 inches above the pot. This prevents the eggs from curdling and separating. Let sit for 30 seconds – do not stir. After 30 seconds use the ladle to gently stir the eggs into the soup.
Garnish with the cilantro and serve immediately.