First, mix your thinly sliced chicken with 2 tablespoons of soy sauce and let it sit. This simple marinade step infuses flavor deep into the meat. It also helps keep the chicken tender and juicy during cooking.
In a small bowl, combine the remaining soy sauce, hoisin sauce, rice vinegar, and cornstarch. Whisk until smooth so there are no lumps. The cornstarch will thicken beautifully once heated in the pan.
Heat a small nonstick skillet and pour in the beaten eggs. Let them set gently, then flip and cook until firm but still soft. Slice into thin strips and set aside for later.
Warm 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken in a single layer. Cook until golden brown and no longer pink, then remove and set aside.
Add the remaining oil to the same pan. Stir in the garlic and ginger and cook briefly until fragrant. This step builds a deep, savory base for the entire dish.
Add the cabbage, carrots, mushrooms, and green onions. Stir-fry until the vegetables are tender but still slightly crisp. Keeping a little crunch gives the dish great texture.
Return the chicken to the pan along with the prepared sauce. Stir continuously as the sauce thickens and coats the ingredients. Gently fold in the egg strips and serve immediately while hot.