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1
Score the skin of each split trotter in a diamond pattern with a sharp knife. Place trotters in a large pot, cover generously with cold water and bring to a full boil. Boil at a hard simmer for 30 minutes, skimming constantly. Drain completely and discard the water. The trotters should show no trace of blood in the runoff; if the water is still heavily clouded and red, extend the boil by 10 minutes.
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2
Return the blanched trotters to a clean heavy pot. Add soy sauce, mirin, sake, sugar and water. Bring to a gentle simmer over moderate heat, then immediately reduce to the lowest flame that sustains a lazy, intermittent bubble. This is where the dish lives or dies: high heat will disintegrate the trotter before the cartilage has fully rendered, yielding pieces that fall apart without the sought unctuous cohesion; the braise must hold a gentle simmer, never a rolling boil, for the full duration.
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3
Braise uncovered, turning the trotters every 45 minutes, for 3 to 4 hours. Skim fat from the surface as needed. At 3 hours, probe the thickest cartilage with a chopstick or skewer: it should meet no resistance and slide through as if entering cold butter. Firm resistance means the collagen has not fully rendered; continue until the cartilage yields completely.
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4
For the tebichi variation, add 100 ml awamori and the juice of two shikwasa during the final hour of braising, stirring to incorporate. The sharpness of the alcohol and citrus cuts through the accumulating richness of the reduced braising liquid.
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5
Remove the pot from the heat. Do not lift the trotters out. Allow them to cool completely in the braising liquid — this cooling period is not optional; the skin continues to absorb the sauce as the gelatin in the liquid sets around the pieces. The surface of the liquid will thicken visibly as the temperature drops, and the skin will deepen to a dark, lacquered mahogany.
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6
Gently reheat trotters in the braising liquid until warmed through. Plate, spoon the reduced braising liquid over as a glaze, and serve with karashi alongside. The skin should be entirely silky and offer no chew; the collagen and connective tissue should be fully translucent and unctuous.