Lightly rinse the dried shiitake mushrooms. Add them to a bowl with the kombu and pour 3 ½ cups of boiling water over them. Let them rehydrate for 30 min.
Meanwhile, cut all the vegetables, taking into consideration their cooking time.
Heat sesame oil in a large heavy-bottom pot on medium and stir-fry the carrots, sweet potato, and daikon radish with brown sugar for about 5 minutes.
Add the sake and let it cook until the alcohol evaporates.
After 30 minutes have passed, remove the kombu and shiitake mushrooms from the water. Cut the shiitake into bite-sized pieces and add them to the pot.
Add the broth, but be careful not to pour in the sediments at the bottom.
Add taro, salt, and soy sauce, and simmer until the veggies soften (20-30 min).
Finish with the crumbled tofu and edamame. Heat it through and taste for salt.
Serve with mitsuba or parsley to garnish and optional rice on the side. Enjoy!