Wash and chop a green onion. Divide the white part and the green part into 2 piles. Set aside.
Crack 2 large eggs in a bowl, beat until smooth. Set aside.
Add 2 tbsps of cornstarch and 3 tbsps of cold water to a small bowl, stir until smooth. Set aside.
Pour 3 cups of vegetable/chicken stock to a pot. Add the white part of the green onion to the pot. Cook over high heat until simmering.
Once simmering, turn heat to medium low, gradually stir in the cornstarch water. Gently but continuously stir the soup until it turns glossy and thicken.
Use a ladle to drizzle the egg to the soup by drawing clockwise circles above the pot. Repeat until you use all the beaten egg.
Add salt, white pepper, and sesame oil to the soup. Gently stir until dissolved.
Transfer to a soup bowl. Garnish with green part of the green onion.