In a wok or saucepan, bring the 4 cups of chicken broth to a boil. Add the white pepper and salt, and the sesame oil if using. Cook for about another minute.
Very slowly pour in the eggs in a steady stream.
To make shreds, stir the egg rapidly in a clockwise direction for one minute. To make thin streams or ribbons, gently stir the eggs in a clockwise direction until they form.
Garnish with green onion and serve.