Place a medium pot or saucepan over medium heat and add the oil. Sauté the sliced scallion whites and minced garlic for 2 minutes until soft and fragrant.
Add the chopped tomatoes. Cook for 5 minutes, stirring occasionally, until they are saucy and falling apart.
Pour the stock, water, and soy sauce (or tamari) into the pot. Bring the mixture to a boil, then reduce the heat to medium-low and let it simmer for 5 minutes.
Sprinkle the ground white pepper over the soup – it tends to cluster, so don't just dump it in. Then stir in the sesame oil and a pinch of salt to season the soup. Taste and adjust the seasoning to your preference.
Next, make a cornstarch slurry by mixing the cornstarch with 2 tablespoons of cold water in a small bowl. Stir the slurry into the soup until the cornstarch is incorporated and the soup thickens slightly. Add extra cornstarch slurry if you want a thicker soup.
While maintaining a gentle simmer, move a soup ladle in a circular motion beneath the soup surface to create a whirlpool. Keep stirring as you slowly pour the whisked eggs into the soup in a thin stream. Stir the soup to break apart the egg drizzle, or leave them undisturbed for longer ribbons – I prefer longer silky egg ribbons. Let the wisps of egg cook for another minute.
Ladle the soup into bowls, and garnish with the reserved green bits of scallion. Serve the soup warm or at room temperature.