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1
Blanch the konnyaku pieces in a pan of boiling water for 2 minutes. Drain and set aside. This step is obligatory: without it, an off-mineral odour persists through cooking. The konnyaku is ready when it has lost its raw, alkaline smell.
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2
Drain the gobo and pat all vegetables dry. Heat the sesame oil in a wide, heavy pan over high heat. Add the chicken pieces skin-side down in a single layer and sear without moving them. Render the fat and develop Maillard browning on the skin. Turn and colour the flesh side briefly. The chicken is ready to proceed when the skin is visibly golden and the pan smells of roasted rather than raw poultry.
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3
This is where the dish lives or dies. Without lowering the heat, add the gobo, renkon, and carrot to the pan. Sauté everything together at high heat, turning frequently, until the cut surfaces of the vegetables show light colour and the pan sounds dry — a sharp, crackling sizzle with no steaming hiss. This 'iri' step evaporates surface moisture, seals the vegetable structure, and builds the roasted character that separates iridori from a simple simmered nimono. If the heat is too low or the pan too crowded, the vegetables will steam and the dish becomes irreversibly pallid.
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4
Add the konnyaku and satoimo to the pan last, stirring to coat them in the seasoned oil. The satoimo goes in after the sturdier vegetables to prevent disintegration. Combine the dashi, soy sauce, mirin, and sake, then pour over the contents of the pan. The liquid should just reach the level of the ingredients without fully submerging them.
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5
Bring to a vigorous simmer, then reduce the heat to medium. Place a drop-lid (otoshibuta) or a cartouche of baking paper directly on the surface to promote even absorption and prevent the vegetables from bobbing. Simmer, turning the pieces occasionally, until the chicken is cooked through and the vegetables are fully tender. The satoimo, when pressed, should yield without resistance.
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6
Increase the heat to medium-high and cook uncovered, stirring gently, until the braising liquid is almost entirely absorbed. The dish is finished when each piece — chicken, vegetable, and konnyaku alike — is coated in a glossy, concentrated glaze and the pan base shows only a thin sheen of syrupy liquid, not a pool. No wet sauce should remain.
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7
Transfer to a serving dish. Bruise the kinome leaves lightly between the palms to release their volatile oils, then scatter over the top. The garnish is done when the faint citrus-pepper fragrance of sansho is perceptible above the dish.