Heat a nonstick skillet over medium heat. Add the ground chicken and chopped onion. Cook, breaking the chicken apart as it cooks, until the chicken is completely cooked through.
Add the minced garlic and grated fresh ginger. Cook for about 2 minutes, stirring frequently, until fragrant.
Add the shredded cabbage to the skillet. Stir everything together and cook for about 7 minutes, stirring frequently, until the cabbage is tender but still has a little crunch.
Add the soy sauce, sesame oil, and rice vinegar. Stir well so the sauce coats the chicken and cabbage.
Taste and season with salt and pepper if needed. Garnish with sliced green onions and sesame seeds, if desired.