Cook the noodles according to package instructions, drain, rinse with cold water to stop cooking, and set aside in serving bowls.

In a soup pot, heat the vegetable oil over medium heat. Add the white parts of the green onions and the minced ginger, sautéing for 1 minute until fragrant.

Add the tomato wedges to the pot and cook for 3-4 minutes, pressing down gently to release their juices and soften them.

Pour in the broth, soy sauce, and sugar. Bring the mixture to a boil, then reduce heat and let simmer for 5 minutes to meld the flavors.

Stir in the cornstarch slurry to slightly thicken the soup, giving it a velvety texture.

While the soup is gently simmering (ensure it is not boiling violently), slowly drizzle in the beaten eggs while stirring the soup in a circular motion to create silky ribbons.

Remove from heat immediately. Stir in the sesame oil and season with salt and white pepper to taste.

Ladle the hot soup and eggs over the prepared noodles and garnish with the reserved green onion tops.