Bring the water and kombu to a simmer, uncovered, over medium heat. Gently simmer the kombu for 3-5 minutes, then remove it. (You may want to reserve it for another use, such as when cooking beans.) Add shoyu, mirin, and salt and simmer for 2-3 minutes. Remove from heat and refrigerate until cool.
Meanwhile, prepare somen according to the directions on the package. After rinsing the cooked noodles in cold water and draining them, place somen into small serving bowls (for this dish, glass bowls are lovely). Gently pour into each bowl about 1 cup cold water and, if desired, arrange a few ice cubes around the noodles. Garnish with a single parsley or watercress spring, a fresh strawberry, or anything simple, cooling, and colorful.
Serve 1 cup chilled dipping broth in small individual bowls, adding 1 tablespoon scallion and 1 teaspoon wasabi paste or grated ginger to each. Dip each bite of noodles into the broth. When dipping broth becomes weak, replace with fresh broth.