Soak dried mushrooms in 2 cups boiling water for 30 minutes. Remove mushrooms and save the stock. Chop mushrooms finely. Place in a bowl with tamari, mirin, and fish sauce, stir to combine.
Heat oil in a skillet, add mushroom mixture with 1 cup reserved mushroom stock. Simmer until all the liquid is absorbed and the mushrooms are very soft, add more stock if needed.
Place strip of nori in onigiri mold at the bottom, add rice, mushroom filling, and more rice. Press mold and release the onigiri from the mold. Garnish the top with a bit of mushroom mixture.