Prep the mushrooms by cutting off the stems and quarter the caps.
Next, we need to make the thickening slurry, mix the corn starch with the 3 tablespoons of cold water until well blended and no lumps. In another bowl, beat the egg. Set both of these aside.
Next, in a small bowl, add the soy sauce, dark soy sauce, and rice vinegar, stir to mix. Set this aside.
In a large sauce pan, add the broth and 1½ cups water, bring to a boil then add the mushrooms and tofu and let boil for 2 minutes. (I did not have tofu on hand and simply omitted that, still worked perfectly.)
Stir the soy sauce mixture into the soup, and season with a few dashes of white pepper or to taste. Give the slurry another stir then stir that into the soup, continue stirring until just slightly thickened, about 1-2 minutes. Turn off the heat but leave on the same burner.
Now gently stir the soup in one direction, and pour the beaten egg into soup in a gently stir and count to 10. Then using the handle end of a spoon or fork, or a pair of chop sticks, stir the soup in the same direction for 3 complete circular motions, this makes the nice egg threads in the soup. Season to taste with chili oil or flakes if desired.
Now the soup is done, ladle into bowls and serve.