How to Make It
Break heads off sardines and remove the small black pellet of innards just beneath each head (they're dried, so this isn't messy). Put cleaned sardines, mushrooms, kombu, and 8 cups water into a medium pot. Cover and chill overnight.
Set pot over medium-low heat and bring to a simmer. When small bubbles form along sides and bottom of pot, but before it actually begins to simmer, remove sardines, mushrooms, and kombu.
Increase heat to high and bring to a boil. Add bonito flakes, pressing down with a spoon to submerge, and return to a boil; then immediately turn off heat. Let flakes settle to bottom of pot, about 15 minutes.
Strain broth through a cheesecloth-lined strainer into a bowl. Wring out all liquid from cheesecloth into bowl. Rinse pot, pour in strained broth, and heat over medium-high heat. Add mirin and soy sauce; simmer 5 minutes.
Make ahead: Up to 2 days, chilled.
Peko Peko catering, Oakland, California