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1
Place the dried hijiki in a generous volume of cold water and soak for 20–30 minutes. The seaweed will triple or quadruple in volume. Drain thoroughly and squeeze firmly with both hands to expel excess water, which would otherwise dilute the simmering liquid. The rehydrated hijiki should feel damp but not wet, and carry a firm, slightly springy resistance.
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2
Heat the sesame oil in a medium saucepan or wide frying pan over medium heat. Add the carrot julienne first and sauté for one to two minutes until the edges begin to soften and a faint caramel sweetness rises from the pan. Add the hijiki and abura-age and continue to sauté, turning everything in the oil, for a further two minutes. The hijiki should glisten and the scent of toasted sesame should deepen — this fat-coating stage builds a complexity that simmering alone cannot produce.
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3
This is where the dish lives or dies. Pour in the soy sauce, mirin, sake, sugar, and water. Stir once to combine. Bring to a gentle simmer over medium heat, then reduce to low. Cook uncovered, stirring occasionally, until the liquid reduces to a glossy, concentrated glaze that just barely pools at the base of the pan — approximately 15–18 minutes. The hijiki must remain distinct and slightly chewy; the moment the liquid is absorbed and the glaze coats every strand without pooling, remove the pan from the heat. Overcooking beyond this point renders the hijiki mushy.
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4
In the final minute of cooking, stir in the shelled edamame. They require no more than 60 seconds in the residual heat of the pan. They are done when they hold their bright, vivid green and yield a clean firmness when pressed between finger and thumb — any dulling to olive signals they have cooked too long.
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5
Transfer to a shallow dish and allow to cool to room temperature before serving. The dish is best served at room temperature or slightly chilled, after overnight refrigeration allows the soy-mirin glaze to integrate fully into the seaweed and tofu. The finished dish keeps refrigerated for 3–4 days.