Soak the dried Shiitake in water overnight to rehydrate. Slice the caps of the Shiitake. Cut off the hard parts of the stem and tear the rest by hand or slice with a knife into small pieces.
Cut the konnyaku into 2cm strips, boil in water, and skim the scum off the top. Thinly shave the burdock root into a bowl of water and skim off the dirt.
Cut the taro into 5mm thick quarters (half moon wedges), gently rub with a pinch of salt, and wash with water to get rid of the slime.
Cut the carrot and daikon radish into 2mm thick quarters. Rehydrate the fu and squeeze the water out.
Cut off the top and bottom of the green beans, slice diagonally, and boil in water with a pinch of salt. Once it looks bright green, drain and put in cold water.
Dice the tofu. Pour some hot water over the fried tofu skin to get rid of excess oil and slice into half.
Add the vegetable stock to the pot and cook the burdock root, daikon radish, carrots, konnyaku, taro, and Shiitake until the hard vegetables become soft. Skim off the scum on the surface while it cooks.
The soup will evaporate, so add hot water or water accordingly, then add the tofu, fried tofu skin, and fu.
Season with soy sauce and mirin.
Boil the Umen noodles in lots of hot water for a short period of time for a chewy texture, drain, put in cold water, and drain well.
Add potato starch dissolved in water to thicken the soup, add the umen noodles, and serve. Garnish with the boiled green beans.