In a medium saucepan, combine chicken broth, water, and chicken bouillon and put on medium-high heat. Add minced green onion, ground ginger, white pepper, soy sauce, and sesame oil and stir until combined.
When the liquid gets to a boil, use a fork to drizzle whisked egg into the saucepan. Continue drizzling egg into the liquid until the desired amount of egg has been added.