Place 4 1/4 cups water and 2 (about 5-inch) pieces kombu in a large saucepan over high heat. When small bubbles start to form (but before it comes to a simmer), remove the kombu. Continue heating until the water comes to a boil.
Add 4 loosely packed cups katsuobushi and remove the saucepan from the heat. Use the tips of a pair of chopsticks to gently press the katsuobushi into the water until it is submerged. Let sit undisturbed for 10 to 15 minutes. (Do not stir, as it will make the dashi cloudy.)
Fit a fine-mesh strainer over a medium bowl, then line the strainer with cheesecloth or a paper towel. Pour the dashi through the strainer. Gather the cloth or paper towel around the katsuobushi and gently squeeze out the remaining liquid; discard the contents of the strainer.
