Combine ¼ cup of the bone broth or chicken broth with the arrowroot powder in a small bowl. Then reserve a handful of the green onions for garnish.
Combine the broth, the rest of the green onions, mushrooms, tamari, ginger, and pepper in a saucepan and bring to a boil. Then add the arrowroot powder mixture, stir, and reduce heat to a simmer. Taste and add salt if needed.
Beat the eggs in a bowl and slowly pour them into the soup while stirring in a circle. Once all the eggs have been added, take off the heat and serve immediately garnished with the reserved green onions.