Put the dried hijiki in a bowl and add about twice as much warm water. Soak for 30 minutes to rehydrate, then drain and rinse.Pour some boiled water over the fried tofu, then julienne into 2cm long strips.Julienne the carrots into 2cm long strips.
Heat a saucepan and add the oil, then add the carrot and hijiki and stir fry over medium high heat. After a couple of minutes add the fried tofu and continue to cook for another couple of minutes.
Mix in the dashi and sugar, cooking over medium heat for 5 minutes.
Add the soy sauce and reduce heat to medium low. Cover with a drop lid (we used a makeshift one of parchment paper here) and simmer until the liquid reduces to about a third. Can be served hot or chilled.