Break the shimeji mushrooms into easy-to-eat pieces, trim off the tough root end, and separate them by hand.
Remove the stems from the shiitake mushrooms by twisting them off from the base. Trim the tough ends from the stems, then thinly slice both the stems and caps.
Cut the aburaage in half lengthwise, then slice thinly.
Thaw the edamame. If using ginger, julienne it into thin strips.
Add the rinsed rice to the rice cooker and add water up to the 2-cup line. Add the dashi powder, sake, mirin, soy sauce, salt, and ginger, then mix well.
Add the shimeji mushrooms, shiitake mushrooms, aburaage, and edamame. Spread everything evenly over the rice. Don’t worry if the mushrooms seem to fill the rice cooker—they will shrink considerably as they cook.
Cook the rice using your regular setting or the quick-cook setting. Once the rice is done, use a rice paddle to gently but thoroughly mix everything together to evenly distribute the seasonings throughout the rice. Serve hot.