Soak the Kombu for a few hours (if possible). Bring water slowly to a boil (over about 10 minutes). Skim and remove the Kombu right before water starts boiling. Add Katsuobushi, bring to a boil, reduce heat and simmer for 30 seconds then kill heat and steep for 10 minutes.
Soak Shiitake for about 30 minutes (room temperature). Squeeze and remove from liquid.
Soak Shiitake and Kombu for about 30 minutes (room temperature). Squeeze and remove from liquid. Bring water slowly to a boil (over about 10 minutes). Skim and remove the Kombu right before water starts boiling.