In a small bowl, mix the cornstarch with water and stir until well blended. Set aside.
Bring the chicken broth and water to a boil in a pot. Add the tomato, white pepper, and salt, then thicken the soup with the cornstarch mixture. Stir the soup with a ladle and turn off the heat.
Swirl the beaten eggs into the soup and immediately stir three times with a pair of chopsticks. Cover the pot with its lid for 2 minutes. The eggs should be cooked and form silken threads.
Serve immediately by dishing the soup into individual serving bowls.
