Whisk together the dashi, sugar, soy sauce, mirin, and salt, and eggs.
Heat the tamagoyaki pan over medium heat. Lightly oil and pour a thin layer of egg over bottom of pan, tilting to cover the surface. As the egg cooks, pierce any bubbles that form. Once set, roll the egg into one side of the pan, move back to the other side, lightly oil again, and pour in more egg just to cover the bottom, including under the rolled egg.
Repeat cooking and rolling until only half of the egg mixture remains. After adding another layer of egg mixture to the pan, place the sheet of nori on top and continue the cooking and rolling process.
Once all the egg mixture has been added, brown the egg roll briefly. Transfer to a bamboo mat, shape, and let stand for 5 minutes before serving.