Place the shiitake in a large soup pot and pour the boiling water on top. Cover and simmer until the mushrooms are soft, about 10 minutes. Remove the shiitake with a slotted spoon. Cut off and discard the stems, and slice the caps into slivers. Return the sliced shiitake to the pot. Add the reserved soybean liquid, ginger, and carrot. Bring to a boil, cover, and simmer for 5 minutes. Add the wakame flakes and soybeans and cook uncovered at a gentle boil for 1 more minute.
Meanwhile, ladle about 1/8 cup of the hot soup liquid into a cup or bowl and dissolve the miso in it. Just before serving, turn the heat to low, add the miso, stir and simmer, without boiling for 2 to 3 minutes. Dissolve and add more miso if desired.
Per serving - 135 calories, 5 g fat (34% calories from fat), 11 g protein, 13 g carbohydrate, 9 g fiber, 0 mg cholesterol, 376 mg sodium