Rinse and soak the Dried Hijiki in plenty of cold water for 20–30 minutes until rehydrated and plumped; drain well and squeeze out excess water.
Meanwhile, peel and cut the Carrot into thin matchsticks (julienne). Pour boiling water over the Aburaage to remove excess oil, drain, squeeze gently, then slice into thin strips.
Heat a wide skillet or saucepan over medium heat and add the Sesame Oil. When fragrant, add the carrot and aburaage and stir-fry briefly until the carrot begins to soften, about 2 minutes.
Add the drained hijiki to the pan and toss with the vegetables for another minute so the flavors start to combine.
Pour in the Dashi to just barely cover the ingredients, bring to a gentle simmer.
Season the mixture with Soy Sauce, Mirin, Sake, and Sugar. Stir to dissolve the sugar and distribute the seasonings evenly.
Reduce the heat to low and simmer uncovered for 10–15 minutes, or until the liquid has mostly reduced and the hijiki and vegetables are tender but not mushy. Taste and adjust seasoning if needed.
Remove from heat and let the dish cool slightly so the flavors meld. Serve warm or at room temperature as a side dish or in bento boxes.
