Heat the sesame oil in a medium pot set over medium heat. Add the onions, ginger, and garlic, and stir and cook until the garlic becomes fragrant, about 30 seconds.
1 teaspoon sesame oil, 6 green onions, 3 slices fresh ginger, 2 cloves garlic
Pour 5¾ cup of the chicken broth and all of the soy sauce into the pot. Turn the heat up to high and bring to a boil.
6 cups low sodium chicken broth, ¼ cup low-sodium soy sauce
In a small bowl, whisk the remaining ¼ cup of chicken broth and cornstarch together. Pour it into the pot and stir to combine.
1 teaspoon cornstarch
Let the soup continue to boil for 5 minutes, then use a ladle to gradually pour in the eggs, whisking constantly. (They will cook instantly when they hit the broth and form ribbons.)
4 large eggs
Taste the broth and add the salt if needed. Serve with additional green onions for garnish.
½ teaspoon kosher salt