In a medium saucepan, combine the chicken broth, soy sauce, and grated ginger. Bring the mixture to a simmer over medium heat.

In a small bowl, whisk together the cornstarch and water to create a slurry. This will thicken the soup.

Slowly pour the cornstarch slurry into the simmering broth, stirring constantly until the soup thickens slightly.

Reduce the heat to low, then slowly drizzle the beaten eggs into the soup in a thin stream while gently stirring in one direction. Cook for 1 minute until the eggs form delicate strands. Stir in the chopped green onions and sesame oil (if using) just before serving.