In a large pot, heat 2 tablespoons of olive oil over medium heat. Add the 2 cinnamon sticks, 1 star anise, lemongrass, ginger, and garlic. Sauté for about 2-3 minutes until fragrant.
Pour in 4 cups of chicken broth and bring to a gentle simmer. Add red pepper flakes if desired. Simmer for about 10 minutes.
Add the bok choy and mushrooms. Simmer for an additional 5-7 minutes until bok choy is tender.
In a small bowl, whisk together the eggs.
In another small bowl, mix cornstarch with cold water to create a slurry. Stir into the broth.
Slowly drizzle in the egg mixture while stirring gently to create ribbons.
Stir in liquid aminos to taste. Remove from heat.
Ladle the soup into bowls and garnish with green onions. Serve warm.