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1
Combine the eggs with dashi, mirin, and soy sauce (for dashimaki) or with sugar, reduced dashi, and soy sauce (for Tokyo style). Beat until fully homogeneous but do not incorporate excess air. The mixture is ready when it flows in a single unbroken stream and the seasonings are indistinguishable from the egg.
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2
Place the rectangular copper tamagoyakiki over medium-low heat. Oil the pan thoroughly with a paper towel folded into a pad, coating every surface including the corners. The pan is at the correct temperature when a drop of mixture sets at the edges within two to three seconds but does not colour.
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3
Pour in roughly one-third of the egg mixture, tilting the pan so it covers the surface in a thin, even sheet. This is the step on which the dish lives or dies: the layer must be allowed to set at the edges and surface while remaining barely fluid at the centre — not raw, not fully cooked — before rolling begins. A fully liquid centre causes layer separation; a fully set layer causes cracking.
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4
Using chopsticks or a spatula, roll the barely-set sheet from the far end of the pan toward you in three or four progressive folds, building a rectangular log. Push the completed roll to the far end. Oil the now-exposed pan surface with the paper towel, including beneath the roll.
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5
Pour in the next third of the mixture, lifting the existing roll so the liquid egg flows beneath it and bonds to it. Allow this layer to reach the same barely-set state as the first, then roll the mass back over it toward you. Repeat with the remaining mixture. Each completed roll should be pale golden — not browned — and the pan should produce a very quiet sizzle throughout.
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6
Turn the finished roll onto a bamboo mat (sudare) immediately while hot. Roll the mat firmly around the egg log and press gently but decisively to form a rectangular cross-section. Hold for two to three minutes as the eggs cool and the shape sets. The roll is correctly pressed when it holds its rectangular form without the mat.
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7
Unwrap and slice crosswise into portions of approximately 2–3 cm. For dashimaki, the cut face should tremble slightly under the knife — a soft, custardy interior with no visible layer separation. For Tokyo style, the face will be firmer and more uniform. Serve at room temperature or slightly warm.