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1
Combine the eggs, finely minced green onion, finely minced carrot, and salt in a bowl. Beat with chopsticks or a fork using minimal strokes — only until the yolks and whites are just unified — so the mixture stays dense and cohesive rather than aerated, which would cause the cooked layers to bubble and tear during rolling. The mixture should be smooth and lightly streaked, not foamy; visible bubbles on the surface indicate over-beating, so allow them to subside before proceeding.
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2
Set a rectangular tamagoyaki pan or non-stick round pan over medium-low heat and apply a thin, even film of oil with a folded paper towel, so the surface glistens without pooling — excess oil will cause the egg to slide and resist bonding between layers. The pan is ready when a drop of egg mixture sets within three seconds without immediate browning.
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3
Pour in enough egg mixture to coat the pan in a thin, even layer. This is where the dish lives or dies: the egg must be allowed to set on the bottom while the surface remains visibly liquid and glossy — not wet, not dry — because this narrow window is the only moment the layer can be rolled without cracking. Too much heat closes the window before the cook can act; too little leaves the centre raw inside the finished cylinder.
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4
Using a spatula or chopsticks, begin rolling the set layer away from the handle in small, tight increments, pressing gently to keep the cylinder compact so no air pockets form that would later open into gaps when the roll is sliced. Push the completed roll to the far end of the pan, then oil the exposed pan surface lightly.
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5
Pour in a second thin layer of egg mixture, lifting the existing roll slightly to allow the new egg to flow beneath it and bond, so each successive layer fuses to the cylinder rather than sitting as a loose wrapper around it. Allow this layer to reach the same just-set state — surface glossy but no longer wet — then roll the existing cylinder back over it, incorporating the new layer; repeat with the remaining egg mixture until exhausted. The finished cylinder should feel firm and spring back slightly under light pressure.
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6
Transfer the roll to a bamboo mat or board and press gently to compact the cylinder, holding the shape for one to two minutes so the residual heat finishes the centre evenly and the roll keeps its form once the pressure is released. Slice into rounds of approximately 1.5 cm; each cross-section should reveal three to four distinct concentric egg layers without gaps, raw patches, or unravelling — the visual proof of correct heat and roll tension.