Heat the oil in a soup pot or wok over medium low heat. Add the tomato chunks and stir-fry for 5 minutes until the tomatoes are softened and start to fall apart.
Add in 1 cup chicken stock, 2 cups water, 2 teaspoons light soy sauce, 1/2 teaspoon sesame oil, 1/4 teaspoon ground white pepper and salt to taste. Bring to a boil, and then lower the heat so that the soup is simmering with the lid on.
Now quickly beat the egg in a small bowl and prepare the cornstarch slurry in a separate bowl.
Use a ladle to slowly swirl the soup in a whirlpool motion. Keep swirling as you pour in the cornstarch slurry until well incorporated. Now pour a thin stream of egg into the middle of the whirlpool as you slowly swirl the soup. This is how you get that pretty egg drop effect.
Serve hot or at room temperature. Ladle the soup into bowls and garnish with chopped scallions and cilantro, if using.