Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the chicken pieces and cook until browned and cooked through, about 5-7 minutes. 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 sliced cabbage, bell pepper, and carrots to the skillet. Stir-fry for about 5-6 minutes until the vegetables are tender but still crisp.

Return the cooked chicken to the skillet. In a small bowl, mix together the soy sauce, rice vinegar, sesame oil, and sugar. Pour this mixture over the chicken and vegetables. Stir well to combine and cook for an additional 2-3 minutes.

Season with salt and pepper to taste. Remove from heat and garnish with sliced green onions and sesame seeds if desired.

Serve hot over rice or noodles.