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1
Beat the eggs gently — do not whisk to a foam — then stir in the dashi, soy sauce, mirin, and salt until fully combined and uniform in colour. Pass through a fine sieve into a pouring vessel. The mixture should be pale gold and entirely smooth.
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2
Set a rectangular tamagoyaki pan (makiyakinabe; copper strongly preferred) over medium-low heat. Lightly oil the surface with a folded paper cloth. Test readiness by letting a single drop of the egg mixture fall onto the pan: it should set within three seconds — not immediately, not after five. Adjust the heat until this is achieved.
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3
Pour one-third of the egg mixture into the pan, tilting to cover the surface in a thin, even sheet. This step decides the dish: the layer must be cooked until the edges are just set and the surface is barely wet at the centre — not runny, not fully dry. Using chopsticks or a bamboo spatula, roll the sheet from the far end toward you in three or four tight folds, then slide the roll to the far end of the pan. Any layer that is too set will not bond to the next; any layer still liquid will collapse the roll.
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4
Re-oil the empty portion of the pan. Pour half the remaining egg mixture into it, lifting the existing roll so the fresh egg flows underneath it. When the new layer reaches the same just-set state as the first, roll back over the existing cylinder from the far end toward you, incorporating it. Push the roll to the far end again. The layers must be added before the existing roll cools and stiffens.
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5
Re-oil and repeat with the final portion of egg mixture in the same manner, rolling the completed cylinder back over the fresh layer to incorporate it. The finished roll should fill the width of the pan, be golden on the exterior with no dark patches, and feel firm enough to hold its shape when nudged with a spatula yet yield with gentle pressure.
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6
Transfer the roll immediately onto a makisu (bamboo sushi mat). Roll the mat around it firmly and hold for one to two minutes to set the cylindrical form and even the cross-section. When the mat is removed, the roll should hold its shape without support. Allow to rest briefly.
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7
Cut the roll crosswise into portions approximately 2–3 cm thick. The cut face should reveal a uniform golden spiral of even layers; the interior should be moist and custardy and, in a correctly made dashimaki, will weep a small amount of dashi at the cut surface. Serve warm, each piece accompanied by a small mound of grated daikon and a few drops of soy sauce.