Begin by preparing all ingredients: slice chicken, shred cabbage, slice bell pepper, and julienne carrots. Mince garlic and ginger.
In a small bowl, mix the soy sauce, oyster sauce, and cornstarch until well combined. Set aside.
Heat a large skillet or wok over medium-high heat and add vegetable oil.
Once the oil is hot, add the sliced chicken. Season with salt and pepper. Stir-fry for about 5 minutes or until the chicken is cooked through and lightly browned. Remove the chicken from the pan and set aside.
In the same skillet, add garlic and ginger. Sauté for about 30 seconds until fragrant.
Add the bell pepper and carrots to the skillet, stir-frying for another 2-3 minutes until they start to soften.
Add the shredded cabbage to the skillet and continue to stir-fry for an additional 2 minutes, allowing the cabbage to wilt but remain crunchy.
Return the cooked chicken to the skillet. Pour the sauce mixture over the chicken and vegetables, stirring well to combine. Cook for another minute until the sauce thickens slightly.
Drizzle with sesame oil if using and give it a final stir.
Serve hot over cooked rice.