Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the sliced chicken and season with salt and pepper. Cook for about 5-7 minutes, or until the chicken is cooked through and golden brown. Remove the chicken from the skillet and set aside.

In the same skillet, add the minced garlic and ginger. Sauté for about 30 seconds until fragrant.

Add the shredded cabbage, bell pepper, and carrot to the skillet. Stir-fry for about 4-5 minutes, or until the vegetables are tender but still crisp.

Return the cooked chicken to the skillet. Pour in the soy sauce, rice vinegar, and sesame oil. Stir everything together and cook for an additional 2-3 minutes to heat through and combine the flavors.

Taste and adjust seasoning if necessary. Serve hot, garnished with chopped green onions and sesame seeds if desired.