Mix together all the sauce ingredients in a small bowl. Set aside.
Place the sliced chicken in a large bowl and pour in half of the the sauce marinade. Mix to ensure every piece is coated with the sauce. Cover and let it marinate in the fridge for at least 2 hours, or overnight (for more flavour).
Add oil to a large skillet over medium high heat.
Add in the marinated chicken and cook for about 5 minutes, while flipping. Add in the onions, cabbage sweet potato, tteok, and the remaining sauce. Cover and let it cook for a few minutes.
Uncover, and keep on stir-frying for about 5-7 minutes, or until everything is cooked through.
Create a small path in the centre of the skillet. Add in the cheese and green onion. Reduce heat to low. Cover, and cook for 2-3 minutes, or until it has melted. Turn off heat, uncover, and wrap that cheese around the chicken. Enjoy!