Heat the vegetable oil in a large pot over medium-high heat. Add the chicken pieces and sear until browned on all sides, about 5-7 minutes. Remove the chicken and set aside.
In the same pot, add the diced onion, garlic, and ginger. Sauté for 2-3 minutes until the onion is translucent.
Return the chicken to the pot. Add the potatoes, carrot, water, soy sauce, gochugaru, gochujang, sugar, and sesame oil. Stir to combine.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 30-40 minutes, or until the chicken is cooked through and the potatoes are tender.
Taste and adjust seasoning with salt and pepper as needed.
Serve hot, garnished with chopped green onions.