Prepare the chicken: Slice the chicken into thin strips, about bite-sized. Dry the pieces lightly with a paper towel so they cook better. Keeping the strips uniform ensures they cook evenly during stir frying.
Make the sauce: In a small bowl, stir together the soy sauce, oyster sauce (if using), rice vinegar, sesame oil, and black pepper until smooth. If you like a thicker sauce, dissolve the cornstarch in water and add it here. Set aside near your stove so you can reach it quickly when needed.
Cook the chicken: Heat 1 tablespoon of vegetable oil in a wok or large skillet over medium-high heat. Add the chicken strips and stir fry for 4–5 minutes, turning often until lightly browned and nearly cooked through. Remove the chicken from the pan and place on a plate.
Cook the vegetables: In the same pan, add the remaining tablespoon of vegetable oil. Add onion, garlic, and ginger, stirring for 1–2 minutes until fragrant. Then add the shredded cabbage and carrot. Stir fry for about 4–5 minutes, stirring often so the vegetables cook evenly and retain a bit of crunch.
Combine and finish: Return the chicken to the pan with the vegetables. Pour in the sauce and stir well to coat everything. Cook for another 2–3 minutes, letting the sauce thicken slightly and the chicken finish cooking through.
Garnish and serve: Sprinkle chopped green onions and sesame seeds over the top. Stir gently and serve hot straight from the pan.
