In a large pot, put chicken pieces, onion, garlic, celery, and pour 6 cups of water. Bring them to boil, and simmer for 40-45 minutes.
Meanwhile make the dumpling. Combine flour, mashed potatoes, egg, and salt in a mixing bowl. Using a fork, break the egg yoke and start incorporating with the flour and potatoes. Knead with your hand until it turns into dough, about 2-3 minutes. Cover and chill in the fridge until ready to use.
When the stock is done, remove the chicken and let it cool. Discard the vegetables reserving the stock in a pot. Shred the chicken and return to the stock pot. Add the carrot slices and bring them to boil. Add the zucchini slices.
Take the dough out from the fridge. Take a chunk off the dough and slightly flatten it with your hand. Tear bit size pieces off from the chunk and drop them into the stock. The dumpling doesn't have to be uniform in shapes and sizes. Try to work fast. When they are done, they will float to the top.
Season the soup with salt and pepper according to your taste if you want to serve as is.
If you want to serve Korean style with the sauce, season the soup lightly with salt and pepper.
Serve this soup warm with kimchi on the side.
For the sauce, mix all the sauce ingredients in a small bowl. Add 1 teaspoonful of the sauce to the soup to season. Add more if needed.