Add the chicken broth, carrot, cabbage, boiled chicken, rice vinegar, coconut aminos, green chili, and sugar to a medium-sized pot and on medium-high heat, bring everything to a rolling boil.
While the soup is coming to a boil, whip the egg and make the arrowroot slurry by combining the arrowroot powder with water and set them aside.
Once the soup comes to a boil, lower the heat to a simmer and add the arrowroot slurry and let the soup thicken. Switch off the heat once the soup thickens to avoid the arrowroot breaking up. Next, drizzle the whipped egg into the soup in a circular motion and leave it undisturbed for about a minute. Then stir the soup to finish up the egg ribbons.
Garnish with scallions and enjoy immediately.
Notes
You can sauté the boiled chicken in 1 tablespoon of oil before adding it to the soup. This will lend it some depth of flavor.
Make sure you don't overheat the soup after you've added in the arrowroot slurry.
To make things quicker, you can prepare the chicken broth, shredded chicken and veggies ahead of time and refrigerate them in separate containers until you're ready to make the soup.