Lightly season the chicken strips with salt and pepper. Warm 1 tablespoon of sesame oil in a large skillet or wok over medium heat.
Pour in the beaten eggs and allow them to set undisturbed for 2–3 minutes. Remove the cooked eggs, roll into a log on a cutting board, and slice into thin ribbons. Set aside.
Raise the heat to medium-high and add another tablespoon of sesame oil to the pan. Stir-fry the seasoned chicken until golden brown and fully cooked, approximately 3–5 minutes. Remove from the skillet and set aside.
Add the remaining sesame oil to the pan. Incorporate the shredded green cabbage, red cabbage, and sliced mushrooms, sautéing for 3–5 minutes until tender yet still crisp.
In a separate bowl, combine the hoisin sauce, soy sauce, Chinkiang vinegar, garlic paste, ginger paste, and cornstarch. Whisk until the mixture is smooth and well blended.
Return the sliced eggs and cooked chicken to the skillet with the vegetables. Pour the prepared sauce over the mixture, stirring to coat all components evenly. Allow the sauce to thicken slightly as it heats through.
Remove from heat and serve immediately, accompanied by your choice of traditional pancakes, rice, or lettuce wraps for a complete meal.
