Perhaps the best part of this surprisingly simple soup is perfecting your "drop" technique. Do you want the egg to cook into skinny strands, thicker ribbons, or tiny shreds? A recipe this quick and easy can be made often, so you and your child can experiment to find your favorite method.
Bring the chicken broth to a simmer in a 2 1/2- to 3-quart saucepan over medium-high heat. In a separate bowl, combine the water and cornstarch, then stir the cornstarch mixture into the simmering broth.
Bring the broth to a boil, then remove it from the heat. Slowly pour in the egg and gently stir it with a fork in one direction only, stirring slowly for long strands of egg, more rapidly for thinner shreds. Add the snow peas, the green onion, and the ham, if desired. Let the soup stand for a few minutes before serving. Serves 4.