In a medium saucepan, combine the chicken broth and water. Bring to a gentle boil over medium heat.
In a small bowl, whisk together the cornstarch and cold water until smooth. Slowly add this mixture to the boiling broth while stirring continuously to thicken the soup.
Reduce the heat to low. In another bowl, beat the eggs until well mixed.
Slowly drizzle the beaten eggs into the soup while stirring gently in a circular motion to create egg ribbons.
Stir in the soy sauce, sesame oil, white pepper, and salt to taste.
Remove from heat and garnish with sliced green onions before serving.