Chop green onion, separating white and green parts.
Bring stock and white onion parts to a simmer in a medium saucepan.
Mix cornstarch with cold water until smooth, then stir into simmering stock until glossy and thickened.
Beat eggs until completely smooth in a small bowl.
Slowly drizzle beaten eggs into soup while gently stirring in a circular motion to form delicate egg ribbons.
Remove from heat and season with salt, white pepper, and sesame oil.
Garnish with green onion tops and serve immediately.