Place the dried shiitake in a bowl and pour in three cups of warm water. Leave to rehydrate.
Peel the radish and carrot, cut into rings then, using a paring knife, shape into spheres.
Peel and mince the garlic and ginger.
Place the beef in a pot, cover with cold water and bring to the boil.
Leave boiling, uncovered, for at least ten minutes.
Drain the beef and rinse thoroughly under the tap.
Clean the pan, dump in the rinsed beef, and add the ginger, garlic and pepper.
Pour in the soy sauce, mirin, about two cups of the mushroom soaking liquid, and add the sugar.
Bring to the boil, cover, lower the heat and simmer for about 40 minutes.
Cut off the stems of the shiitake and discard (or reserve for another use). Cut the caps into quarters.
Add the radish, carrot, chestnuts and shiitake to the beef. Stir.
Continue simmering until the beef is literally falling off the bones.
Taste the sauce, adjust the seasonings, if needed.