Put chicken pieces in a large pot and add enough water to cover. Add ginger and bring water to a boil; reduce heat to medium and simmer for 10 minutes. Drain water and discard ginger.
Mix 1 1/2 cups water, soy sauce, sugar, hot pepper paste, hot pepper powder, sesame oil, and garlic into chicken; cook and stir over medium heat for 10 minutes.
Stir potatoes and carrot into chicken mixture; cook for 5 minutes. Add onion, salt, and black pepper; mix well. Cook stew until heated through and chicken is no longer pink in the center, about 5 minutes more. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C). Garnish stew with green onions and sesame seeds.