Prepare the shepherd’s purse by thawing it out in a colander. When it’s completely thawed, use your hands to gently squeeze the water from it. Chop the leaves into small pieces. Set aside.
Prepare, the silken tofu by cutting it into ½-inch cubes. Set aside. It can be tricky to keep them in a cube shape since the silken tofu is delicate, so don’t worry if they aren’t perfect.
Heat the chicken stock in a medium pot or wok. Add the salt, sesame oil, and ground white pepper. Let everything come to a slow simmer.
Stir up your cornstarch and water mixture since the cornstarch settles at the bottom of the bowl when left standing. Turn the heat down, and use your metal hoak or soup ladle to stir the soup in a circular motion so the soup is moving and swirling. Slowly drizzle all of the cornstarch slurry into the soup while stirring. The trick to thickening the soup with cornstarch is to turn the heat down slightly and keep the soup moving so the cornstarch does not form clumps.
As you continue stirring, turn the heat back up to get the soup to a very low simmer. Check the soup for seasoning and add more salt if needed. Don’t worry if the soup tastes a little saltier than you’d like at this stage, because the Shepherd’s purse and the silken tofu are both unseasoned.
Simmer the soup for a minute, and add the chopped shepherd’s purse. Stir it gently until the leaves are well distributed.
Next, gently add the silken tofu cubes into the soup, and stir, taking care not to break up the tofu. You want to ensure that the tofu and shepherd’s purse are uniformly distributed in the soup and that both are heated evenly. The soup should start to simmer in about 2 to 4 minutes. At this point, you can add a bit more cornstarch slurry if you like a thicker soup, but keep in mind that the soup will thicken more as it cools.
Beat the egg whites briskly for about 10 seconds until the white is broken up and just starts to bubble.
Next, take your ladle or hoak and move it in a wide, steady swirling motion around the perimeter of the pot or wok until the soup is moving. Slowly drizzle the egg white into the soup.
At this point, adjust the heat so the soup is simmering. Taste the soup again, and season to taste with salt, white pepper, and sesame oil if needed. (Sesame oil and especially white pepper enhances the taste of the Shepherd’s purse, so you can add more or simply put these condiments on the table so they can be added as needed.)
Ladle the soup into bowls to serve or pour the soup into a larger family style soup bowl to serve at the table.