Heat the olive oilover medium-high in a large saucepan or pot. Add cinnamon sticks, anise, lemongrass, ginger, garlic, and red pepper flakes and cook, stirring frequently, until spices are very fragrant, about 3 minutes.
Add the chicken broth and liquid aminos and stir well. Bring mixture to a full boil, then reduce the heat, cover, and simmer for 15 to 20 minutes.
While the broth is simmering, saute the bok choy and mushrooms in a separate skillet. To do so, heat 3 tablespoons of olive oil in a skillet over medium-high and saute the veggies until browned and softened, about 5 to 8 minutes. Once cooked, transfer veggies to the broth.
Taste the broth for flavor. Add more liquid aminos (or miso paste) if desired. Remove the ginger rounds, cinnamon sticks, anise, and lemongrass stalks from the broth using a slotted spoon, and discard.
Add 1 tablespoon of cornstarch to a small bowl and pour in 1/3 to 1/2 cup of the hot broth. Stir well until dissolved.
Transfer the cornstarch mixture to the pot with the broth and stir well, leaving the broth at a very gentle simmer.
Add eggs to a small bowl, along with the remaining (1/2 tablespoon) cornstarch. Whisk together until well-combined.
Slowly pour the egg/starch mixture into the simmering broth through the tines of the fork. Do this a little bit at a time, whisking the broth between pours. Once all of the egg has been poured into the soup, allow broth to sit at low heat for a couple of minutes, whisking occasionally, to ensure egg cooks all the way.
Serve the egg drop soup with freshly chopped green onion, and enjoy!
Notes
*Replace chicken broth with vegetable broth to make this vegetarian.
**You can replace cornstarch with tapioca starch