Gently rinse the kombu piece. Place it in a medium pot with the water and gently simmer for 10 minutes. Don’t let it boil, or the kombu flavor will turn bitter.
Soak the wakame in a small bowl of warm water for at least 5 minutes to rehydrate.
Remove the kombu from the soup. In a small bowl, stir the miso paste together with some of the hot broth until the mixture is smooth, then stir it back into the soup.
Drain the wakame and add it to the soup pot along with the scallions and tofu. Simmer over very low heat for 1 to 2 minutes. Season, to taste, with tamari.