Soak the dried shiitake mushrooms in a bowl of warm water for at least 30 minutes. Then drain, reserving the liquid.
Cut off the stems and finely chop the caps.
Pour some of the soaking liquid into a saucepan and add sugar, mirin, soy sauce, and sake. Bring to a boil.
Add the carrot and shiitake and simmer for 3–4 mins until almost all the liquid is absorbed. Remove from the heat and let cool.
While the rice is still warm, fold in the cooked carrot and shiitake. Dip your hands in the vinegar and then take some rice in your right hand and squeeze the rice to make it oblong and bite-sized.
Stuff a ball of rice into each bag and fold in the edge (optional). Leave the tofu bag open and garnish with salmon roe, shiso leaves and scallions (optional).