1. In a bowl, cover the hijiki with warm water and let stand for 1 hour. Drain, pressing out any excess water. In a small bowl, combine the soy, mirin, sugar and dissolved dashi.
2. Heat the vegetable oil in a saucepan. Add the carrots and fried tofu and cook over high heat for 1 minute. Stir in the hijiki. Add the soy mixture and simmer over moderately low heat, stirring occasionally, until the carrots are tender and the liquid is absorbed, about 15 minutes. Transfer the hijiki salad to a bowl and refrigerate until chilled, 1 hour.
3. In a small bowl, whisk the vinegar with the sesame oil. Add the dressing to the salad and toss to coat. Sprinkle with sesame seeds and serve.
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