Heat a saucepan over moderate heat. Add all but 1/4 cup of the broth to the saucepan; set the 1/4 cup of broth aside.
To the saucepan, add salt, ginger, pepper, and white parts of the scallions. Bring to a rolling boil.
In the meantime, mix 1 tsp of the corn starch into the reserved 1/4 cup of broth; whisk with a fork until the corn starch has dissolved. Bring the broth to a low simmer, and slowly add it to the broth, stirring to blend.
In a small bowl, whisk the eggs and remaining corn starch together until corn starch has dissolved.
With a ladle, create a bit of a whirlpool in the broth by stirring it in a circle. Slowly drip the egg mixture into the whirling broth; the egg should turn into thin ribbons of cooked egg.
Remove the pot from the heat and let it sit for 15 seconds. Spoon the soup into bowls, garnish with the green parts of the sliced scallions, and serve immediately.