Bring the stock to a bare simmer with the ginger. Slide in the chicken breasts and poach gently for 12 to 14 minutes until just cooked. Do not boil; boiled breast is dry breast.
Lift the chicken out, rest 5 minutes, then shred with two forks.
Stir the cornstarch slurry into the simmering stock until it turns lightly silky.
Kill the heat. Stir the soup in a slow circle and pour the beaten egg in a thin stream against the direction of the swirl. Ribbons, not clouds.
Return the chicken, season with white pepper and salt to taste, finish with sesame oil and scallions.