In a large pot, bring chicken broth to a boil over medium-high heat. Add carrots, mushrooms, and scallions. Reduce heat to low and simmer for 10 minutes.

In a small bowl, whisk together cornstarch and cold water until smooth. Add to the soup and stir until the soup thickens slightly.

Slowly pour in the beaten eggs, stirring constantly with a spoon in a circular motion. Cook for 1 minute, then remove from heat.

Stir in white pepper and sesame oil. Ladle into soup bowls and garnish with chopped scallions.