Bring the broth to a simmer over medium-high heat in a large saucepan. Add the mushrooms, chicken, soy sauce, vinegar, and white pepper. Continue to simmer for 5 minutes.

In a small bowl, whisk together the corn starch and cold water to make the slurry. Add it to the soup and stir well. Simmer for 5 minutes or until the soup starts to thicken.

Pour the beaten eggs into the soup in a steady stream while gently stirring it.

Add the tofu and green onions, stir and remove from heat. Serve immediately.