In a small saucepan, whisk the broth, ginger, white pepper, soy sauce, and cornstarch together, over high heat, until no lumps remain. Bring to a boil, occasionally stirring.
Whisk eggs together in a separate bowl.
Once soup is bowling, remove from heat. Then, while whisking the soup in a circular motion, slowly pour in the eggs, to create egg ribbons.
Stir in sesame oil, and top with green onions. Serve immediately.