Wipe away any dirt from the kombu with a paper towel, being careful not to rub off the white powdery deposits on the seaweed. Place the kombu and water in a saucepan, and allow it to soak for 30 minutes to become soft.
Remove the kombu from the water, and cut several lengthwise slits into the leaf. Return the kombu to the water, and bring it to a boil. As soon as the water begins to boil, remove the kombu to prevent the stock from becoming bitter.
Stir the bonito flakes into the kombu-flavored water, bring back to a boil, and take the pan off the heat. Allow the water to cool. When the bonito flakes have settled to the bottom, strain the dashi through a strainer lined with cheesecloth or a coffee filter.