Turn the heat off and give the soup a few good stirs to let it cool just a little bit. Then stir again to create a gentle whirpool, pour in your whisked eggs, and let the gentle heat do its magic to cook the eggs. Stir gently again once or twice to distribute the eggs.
You want the soup at a temperature where the egg just sets, which is what gives it that silky texture. If the egg overcooks, then it takes on a chewier more scrambled texture, but the starch does help to prevent overcooking.