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Prepare the Sauce: In a small bowl, whisk together the soy sauce, oyster sauce, hoisin sauce, cornstarch, chicken broth, and sesame oil until smooth. Set aside.
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Cook the Noodles: Cook the chow mein noodles according to package instructions. Drain and set aside.
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Cook the Chicken: Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Season the sliced chicken with salt and black pepper, then add it to the skillet. Stir-fry for 4-5 minutes, or until cooked through. Remove the chicken from the skillet and set aside.
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Stir-Fry the Vegetables: In the same skillet, add the remaining 1 tablespoon of oil. Add the bell pepper, carrot, cabbage, bean sprouts (if using), green onions, garlic, and ginger. Stir-fry for 3-4 minutes until the vegetables are tender-crisp.
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Combine Ingredients: Return the cooked chicken to the skillet, along with the cooked noodles. Pour the sauce over everything and toss to combine, ensuring everything is evenly coated. Cook for an additional 2-3 minutes, allowing the sauce to thicken slightly.
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Serve: Serve the chicken chow mein hot, garnished with extra green onions if desired.