This soup is very versatile and makes a lot, so plan on leftovers (you may need to add extra broth the next day as the noodles suck up all the liquid overnight). You can use whatever vegetables you have on-hand instead of the carrots and bok choy. See the notes for some additional options.
Heat the sesame oil in a large, non-stick soup pot. Add the ginger and garlic and cook for one minute. Add the water, wakame, carrots, and dried mushrooms and bring to a simmer. Cover and simmer for 15 minutes, or until mushrooms are tender. Add the edamame and cook for another 5 minutes.
Add the noodles and the bok choy, cover, and cook until noodles are tender, about 7 minutes.
Place the miso and wasabi in a bowl and add about 1/2 cup of the hot soup broth. Stir or whisk until there are no lumps and then add it back to the pot and heat through but do not boil. Taste and add more miso or wasabi as needed.
A little sesame oil gives the broth a richer flavor, but if using it is not an option, cook the garlic and ginger in a teaspoon or two of water instead.Whole dried shiitaki mushrooms look nice in this soup but may be hard to chew. You can cut them in pieces with a pair of kitchen shears after they've softened. If you happen to have fresh mushrooms, you can use about 5-8 ounces.Most buckwheat soba noodles found in the U.S. are not gluten-free. If necessary, you can substitute gluten-free pad thai noodles or spaghetti. If you're avoiding pasta, you can substitute about 2 cups of cooked brown rice or other grain; add more as necessary if the soup is too "soupy."If using miso from an Asian grocery, check ingredients carefully to make sure fish (bonito) isn't in the ingredients. To reduce sodium, look for low-sodium miso in natural food stores.