In a medium bowl, whisk together hoisin sauce, low-sodium soy sauce, rice vinegar, minced garlic, grated ginger, cornstarch, sesame oil, freshly ground black pepper, and mirin. Set aside about ½ cup of the marinade for later use.

Place the thinly sliced chicken breasts into the bowl with the remaining marinade, coat well, and let marinate for 10-15 minutes at room temperature.

Heat a large skillet or wok over medium-high heat and add vegetable oil. Cook the marinated chicken in batches for about 2-3 minutes until golden and cooked through. Remove and keep warm.

In the same skillet, add more oil if needed and sauté the sliced shiitake mushrooms for about 4-5 minutes until browned and tender.

Pour the beaten eggs into the skillet, cooking for about 2-3 minutes until set; remove and keep warm with the chicken.

Add the sliced cabbage to the skillet and stir-fry for about 2-3 minutes until just wilted, retaining some crunch.

Return the cooked chicken, mushrooms, and eggs back into the skillet with the cabbage, drizzle with reserved marinade, and stir to combine.

Garnish with thinly sliced green onions and serve immediately with warm tortillas, Mandarin pancakes, or rice.