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1
Score a shallow cross-cut into one flat face of each daikon round. Place the rounds in a pot, cover with rice washing water, and bring to a gentle simmer. Cook for 20–25 minutes. The daikon is ready when a skewer passes through without resistance and the rounds have lost their raw, sharp smell.
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2
Blanch the konnyaku in boiling water for 3 minutes to remove its mineral odour; drain and set aside. Blanch the atsuage in boiling water for 2 minutes to draw off excess frying oil; drain. Pre-boil the beef tendon in plain water until it yields to a skewer — this may take 60–90 minutes. Thread the tendon on bamboo skewers. Discard all blanching liquids.
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3
Combine the dashi, dark soy sauce, mirin, and sake in a wide, heavy pot. Bring to a bare simmer. Taste: the broth should be seasoned to about two-thirds of its intended final depth — it will concentrate and deepen over the hours of cooking. Adjust if necessary, but err toward restraint at this stage.
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4
Add the daikon, konnyaku, beef tendon, and hard-boiled eggs to the broth — the densest, longest-cooking elements first, arranged so that the scored face of the daikon faces down into the liquid. Bring to the gentlest possible simmer: a bubble should break the surface only occasionally. This is where the dish lives or dies — a rolling boil will cloud the broth irreparably and toughen every protein in the pot; the heat must never exceed a trembling murmur for the entirety of the cook.
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5
After one hour of simmering, add the chikuwa, atsuage, and kinchaku. Replenish the broth if needed with additional warm dashi — never plain water — to maintain the level just covering the ingredients. Continue simmering over the lowest heat for a further 3–4 hours. At the two-hour mark, the daikon should be translucent to its core and amber-stained throughout; press a round between two fingers — it should yield completely with no firm centre.
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6
In the final 30 minutes of cooking, add the hanpen triangles. They require only brief immersion; longer cooking will dissolve their cloud-like, yielding texture. The hanpen is ready when it has puffed slightly and feels pillowy when pressed — it should hold its shape but offer no resistance.
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7
Taste the broth and adjust seasoning with additional dark soy sauce if required. Ladle the broth into deep bowls, arranging a selection of the oden ingredients in each. Serve the karashi mustard separately for each diner to stir directly into the broth.