For the chilled noodle soup, put all the ingredients of the soup in a pot. Bring to simmer, and cook for 5 minutes over low heat. Strain the soup into a bowl and discard the kombu seaweed and bonito flakes. Chill the soup in a refrigerator completely.
For the sesame eggplant, cut off the tip of an eggplant and cut it in half lengthwise. Using a sharp knife, score the skin of eggplant 1/4 inch deep diagonally. Brush them with sesame oil evenly. Place them in a microwave-safe plate and wrap it tightly. Microwave it for a couple minutes until they get tender. (My 700 watts microwave takes about 3 minutes, increase or decrease the cooking time according to your microwave power.)
In a small pot, combine soy sauce, mirin, and water. Bring it to a boil. Pour it over the eggplants to marinade. Chill it in a refrigerator. Flip them occasionally.
Bring a large pot to boil for the noodle. Cook the somen noodle according to the instruction of the package. Drain the pot and rinse the noodle with ice water. Once the noodle is chilled, strain it completely.
Divide the noodle into two serving bowls and pour the chilled noodle soup. Top with eggplants, shiso, grated daikon, grated ginger, and chopped green onion.
