Mince the ginger and garlic, and thinly slice the scallions, separating the white and green parts.
In a medium pot, combine the chicken broth, ginger, garlic, and the white parts of the scallions.
Add the chicken breast to the pot and bring to a gentle simmer over medium heat; poach for 12 to 15 minutes until cooked through.
Remove the chicken, shred it with two forks, and set aside.
Whisk the arrowroot powder with a tablespoon of water to create a slurry, then stir it into the simmering broth until slightly thickened.
Stir in the tamari, white pepper, sea salt, and the shredded chicken.
Whisk the egg in a small bowl, then slowly pour it into the soup in a steady stream while stirring the broth in a circular motion to create silky ribbons.
Remove from heat, stir in the toasted sesame oil, and garnish with the green scallion tops.