Soak kombu for 24 hours in cold water. Remove and discard water. Cut into very thin strips. Place in a pan with 2 cups water, sake, and vinegar. Bring to a full boil. Lower heat and let simmer until liquid is reduced by half, add tamari, mirin, and brown sugar. Bring back to a boil over medium heat and let bubble (watch carefully) until all liquid is absorbed and you have a thick glaze. Stir in sesame seeds.
Place strip of nori in onigiri mold at the bottom, add rice, kombu filling, and more rice. Press mold and release the onigiri from the mold.