Add dried woodear mushrooms/black fungus mushrooms and 2 cups of hot water to a large bowl. Let stand for about 30 minutes to reconstitute. Once reconstituted, drain and rinse the mushrooms. Remove or cut out any hard parts. Layer the mushrooms one on top of another and roll into a bundle, then slice into very fine strips. You may also purchase them pre-cut, which I prefer.
In another medium bowl, combine finely minced chicken with cornstarch, soy sauce, mirin (or water), and white pepper. Let marinate while preparing other ingredients.
Slice all other vegetables and tofu into thin strips. Enoki mushrooms come in a small package with the roots still attached. With the packaging still on, cut the bottom 1/4-1/3 (the dirt and roots) off. Remove the mushroom tops and lightly rinse any additional dirt off.
Preheat the Instant Pot on HIgh Saute. Add the carrots, enoki mushrooms, bamboo shoots, woodear mushrooms, shiitake mushrooms, enoki mushrooms, garlic, ginger, green onions, chicken, and chicken broth.
Lock the lid, turn the knob to sealing, and cook on manual high pressure for 5 minutes.
While the soup is cooking, combine in a liquid measuring cup: soy sauce, vinegar, cornstarch, white pepper, and sugar. Whisk the slurry together with a whisk.
After the 5 minutes have elapsed, perform a quick release. Once the pin has dropped, open the lid and turn the Instant Pot to High Saute.
Whisk the slurry again if it has settled. While stirring the soup, pour the cornstarch mixture into the soup and let thicken, about 2-3 minutes. Add tofu, and stir, then turn off the Instant Pot.
In the same liquid measuring cup, beat two eggs. Without stirring the soup, slowly drizzle a thin stream of eggs in a circular motion into the pot. Do not stir. Add sesame oil and wait 30 seconds.
Gently fold the ingredients together by "pulling" the soup from the outsides of the Instant Pot to the middle, about 4 times.
Serve by topping each bowl with a drizzle of additional sesame oil, green onions, white pepper, and crushed red pepper for an additional kick.