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1
Whisk the eggs into the cold dashi until fully combined. Sift in the flour and whisk to a smooth, very thin batter — it should flow like single cream, with egg and dashi clearly dominant over flour. Rest the batter briefly while the pan heats. The batter is ready when it coats a finger in a barely-there film.
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2
Set the takoyaki-ki (cast-iron or copper mould pan) over medium-high heat. Grease every hemispherical mould generously with neutral oil, reaching all inner surfaces; the oil must shimmer and be fully hot before batter is added, or the balls will not release cleanly on rotation.
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3
Pour the batter into each mould, filling just above the rim so the wells overflow slightly into one another. Drop one piece of precooked octopus into the centre of each well. The piece must sit flush; if it protrudes, it will prevent a true sphere from forming.
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4
This is where the dish lives or dies. Watch the edges of each ball: when the batter has set to a pale, opaque ring around the lower hemisphere — still liquid at the centre — drive a thin metal skewer under the edge of each ball and rotate it 90 degrees in one clean movement. Too early and the batter tears apart; too late and the bottom carbonises before the sphere can form. Professionals rotate three to four times, building up smooth, even layers, until a perfect golden sphere is achieved on all sides.
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5
Continue cooking, rotating as needed, until the exterior is evenly golden and crisp. The finished ball should feel lightly resistant when nudged with the skewer — a thin shell enclosing a still-liquid interior. Transfer immediately to a serving dish or tray.
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6
Apply toppings in strict order while the balls are still radiating heat: okonomi sauce first, then Japanese mayonnaise in a crosswise drizzle, then a scatter of aonori flakes, and finally katsuobushi. The bonito shavings should lift and wave in the rising heat — this is the visual sign that the takoyaki are at the correct serving temperature. Serve at once; the liquid interior sets as the balls cool.