Combine the water and kelp in a large pot. Bring the water to a boil, removing the kelp just before water boils since it emits a strong odor. If the fleshiest part of the kelp is still tough, return it to the water for a few more minutes, along with a little cold water. (Soft kelp means sufficient flavor has been extracted.) Remove the kelp and bring stock to a full boil.
Add 1/4 cup cold water to bring the temperature down quickly and add the bonito flakes. Bring to a boil, and then immediately remove from the heat. (If bonito flakes boil too long, the stock becomes bitter.) Allow the flakes to settle to the bottom of the pan, then filter the stock through cheesecloth.
This recipe yields about 2 quarts.