Bring 5 to 6 cups of water to a rolling boil in a medium pot over medium-high heat. Once the water is boiling, add the chicken pieces and parboil for 1 minute to remove impurities. Drain the water completely and set the chicken aside.
In a clean pot, combine the parboiled chicken, prepared sauce mixture, and 1 cup of water. Stir gently to coat the chicken evenly. Cover and bring to a boil over medium-high heat, allowing the flavors to infuse for about 10 minutes.
Add the potatoes, carrots, and onion to the pot. Stir lightly to mix, then cover again and continue boiling for an additional 7 minutes. Reduce the heat to medium and give the stew a gentle stir to reposition the chicken and vegetables, ensuring even cooking. Add the sliced perilla leaves and simmer for another 8 minutes, or until the chicken is fully cooked and the potatoes are tender.
Once done, remove from heat and garnish with sliced green onions and toasted sesame seeds. Serve the stew piping hot with a bowl of steamed white rice for a comforting and spicy Korean meal.