Bring the chicken broth, ginger, salt and pepper to a simmer in a 3+ quart pot.
Make a slurry with the cornstarch and water, and slowly mix into the broth. Bring to a boil, and cook just a minute or two until the broth has thickened a little bit, then lower heat to a gentle simmer.
Slowly drizzle in the whisked eggs while gently stirring the broth in a circular motion.
Stir in the sesame oil, serve topped with green onions.
Notes
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