Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the sliced chicken and season with salt and pepper. Stir-fry for about 5-7 minutes, or until the chicken is cooked through and no longer pink.
Add the minced garlic and ginger to the skillet, stirring for about 30 seconds until fragrant.
Toss in the shredded cabbage, julienned carrots, and sliced bell pepper. Stir-fry for an additional 3-4 minutes until the vegetables are tender-crisp.
Pour in the soy sauce, oyster sauce (if using), and sesame oil. Stir everything together and cook for another 2 minutes to combine the flavors.
Remove from heat and garnish with chopped green onions before serving.