Squeeze the softened kombu of any excess moisture and slice into thin 3 mm strips. Add to a wide frying pan or shallow saucepan.
Add the sake, mirin, sugar, and vinegar — hold back the soy sauce. Bring to a gentle boil, then cover with a lid and simmer over medium-low heat for 10–15 minutes, until the kombu is soft.
Uncover and pour in the soy sauce. Stir, replace the lid, and simmer for another few minutes so the kombu absorbs the soy.
Take the lid off and add the honey. Turn the heat up slightly and stir often as the remaining liquid cooks away — the kombu should be dark, glossy, and thickly coated.
Turn off the heat. Sprinkle in the toasted sesame seeds and stir through.
Cool completely, then transfer to a clean sealed container. Keeps in the fridge for up to 2 weeks.