Cook the Aromatics - In a large pot, heat the vegetable oil. Add the garlic and ginger, and saute for 30-seconds.
Saute the Chicken - Add the sliced chicken, and saute until cooked through, about 2 minutes.
Simmer the Soup - Add the chicken stock and bring to a boil over medium-high heat, then reduce to a simmer over medium-low heat. Add the mushrooms, bamboo shoots, vinegar, soy sauce, sesame oil, honey, and salt, and stir to combine. Simmer for 5 minutes. Add tofu and cook for 1 minute.
Thicken the Consistency - In a small bowl, whisk together cornstarch and water. Gradually add to the soup, constantly stirring until the consistency is slightly thickened, 1 to 2 minutes.
Add the Egg - Turn off the heat and drizzle in the whisked egg. Use a spoon to stir the soup using figure-eight motion until you see strands of cooked egg appear.
Add White Pepper - Stir in the white pepper. Season with salt, pepper, and vinegar to taste.
To Serve - Portion out the soup and garnish with green onions, cilantro, and chili oil if using.
Notes
MAKE IT GLUTEN-FREE:Substitute gluten-free tamari or coconut aminos for soy sauce. Use red wine vinegar or distilled vinegar if your Chinese black vinegar is not gluten-free.
Make it VEGETARIAN: Add more mushrooms or tofu to replace the chicken. Use vegetable stock or broth. Omit the egg for a vegan version.
Black Vinegar Substitutes:Use distilled white vinegar or red wine vinegar. Add 1 teaspoon at a time, taste, and gradually add more as desired. Additional soy sauce can be used to balance the taste. Worcestershire sauce can be used, 1 teaspoon at a time to taste.