Scrape the burdock skin, shred finely into shavings and soak in water. Chop the carrot roughly or into thin batons. Cut the pork into 2 cm lengths. Shred the shimeji mushrooms.
Cut the konnyaku roughly with a spoon and blanch for about 2 minutes. Slice the taro root into 5 mm thick-half moons. Slice the leek diagonally into 5 mm.
Heat oil in a pan. Add and fry the burdock root, carrot, konnyaku and pork over a medium heat. Stir and add dashi stock. After bringing to the boil, skim off the scum on the surface.
Add the soy sauce and sake and cover. Cook over a lowish heat for 15 minutes. Combine the dumpling ingredients in a bowl and mix well with a spoon.
Boil water in a small saucepan and scoop the dumplings with a spoon. Drop the dumplings in the water and cook for about 5 minutes. Drain in a colander.
After 15 minutes add the dumplings and miso. Reduce the heat to low and cook for further 5 minutes. Add the taro root, shimeji mushrooms and Japanese leek and cook for 5 minutes.