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1
Place the kombu squares in a saucepan and cover with fresh cold water. Bring to a gentle simmer over medium heat and cook, uncovered, for 15 minutes. The kombu should have softened noticeably and lost its rigid, leathery resistance. Drain and return the kombu to the pan.
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2
Add the soy sauce, mirin, sake, and sugar to the pan. Set over low-to-medium heat and bring to a steady simmer, uncovered. Stir only occasionally — frequent disturbance will break the kombu pieces. This is where the dish lives or dies: maintain a consistent, active simmer for 20–25 minutes, reducing until virtually all liquid has been expelled and the kombu is coated in a thick, sticky, lacquer-like glaze. If the pan is left insufficiently reduced, the tsukudani will be watery, its preservation compromised, and its flavour diluted; if pushed too far without attention it will scorch. The correct endpoint is a pan that is nearly dry, with the kombu pieces visibly glossy and clinging together.
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3
Remove the pan from the heat. Scatter the sesame seeds over the kombu and fold them in gently. Allow the tsukudani to cool completely in the pan. As it cools, the glaze will set further and the kombu will take on a deep, lacquered appearance.
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4
Transfer to a clean jar or covered container. Store refrigerated for up to 2 weeks. Serve in tablespoon-sized portions alongside plain cooked rice. The concentrated sweet-salty-umami register is calibrated for this small measure; larger portions are overwhelming.