In a large saucepan, combine the kombu with 8 cups of the water and let stand at room temperature until the kombu starts to soften, about 30 minutes.
Bring the water to a bare simmer over moderate heat; tiny bubbles will form on the bottom of the saucepan. Remove from the heat and discard the kombu. Add the remaining 1/2 cup of cold water to the saucepan, then add the bonito shavings and bring just to a simmer. Immediately strain the dashi through a fine sieve and use right away.