Rehydrate the dried shiitake mushrooms in water for 2 to 3 hours, or until soft. Strain and reserve ¼ cup (60 ml) of the soaking water for later as it is packed with umami. Cut the mushrooms in half if too large.
Soak the koya tofu in plenty of water for 10 minutes. Squeeze out excess water and cut each tofu piece into quarters.