Start by heating a little oil in your skillet and pouring in the beaten eggs. Cook until set, then remove and slice into thin strips. This adds protein and texture without overwhelming the dish.
Add remaining oil and sauté the chicken strips until lightly browned and cooked through. This ensures tender pieces that soak up the sauce perfectly.
Add mushrooms, cabbage, and grated ginger to the skillet. Stir-fry until vegetables are just tender, keeping a slight crunch for texture.
Mix soy sauce, hoisin, sesame oil, and cornstarch together. Pour over the chicken and vegetables, tossing to coat. The sauce will thicken slightly and cling to each ingredient.
Return the sliced eggs to the skillet and gently fold into the mixture. This brings all the flavors together beautifully.
Warm your pancakes or tortillas, spoon in the Moo Shu Chicken, and garnish with green onions. Roll or fold and enjoy immediately.