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1
Place the whole, uncut kabocha in a microwave and cook on full power for 2–3 minutes to soften the skin slightly. Transfer to a stable cutting board lined with a folded towel. Using a heavy cleaver and firm, deliberate strokes, halve the kabocha; scoop out and discard the seeds and fibrous core. Cut the flesh into 3–4 cm chunks, retaining the dark green skin on every piece. Leave one flat edge on each piece where possible. The pieces are ready when they are uniform in size and the seed cavity is clean.
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2
Select a wide, shallow pan just large enough to hold all the kabocha pieces in a single layer. Arrange the pieces skin-side down in the cold pan. Pour over the dashi at room temperature; the liquid should come approximately level with the top of the pieces. Add the soy sauce, mirin, and sugar. Do not bring to a boil before the kabocha is in the pan. The arrangement is correct when no piece is stacked and the broth barely covers the flesh.
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3
This is where the dish lives or dies. Set an otoshibuta (drop lid) — a lid slightly smaller than the pan's interior diameter, or a round of dampened baking parchment cut to fit — directly onto the surface of the kabocha and broth. Place the pan over medium-low heat and bring the liquid slowly to a gentle simmer. Maintain that simmer steadily; a rolling boil will disintegrate the flesh before the flavour has penetrated. The drop lid keeps the pieces submerged and the broth circulating evenly over every surface. The dish is at the correct stage when a quiet, steady murmur is audible and wisps of steam escape from the edges of the otoshibuta.
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4
Simmer for 15 minutes, then test a piece by inserting a fine skewer or the tip of a paring knife into the thickest part of the flesh. The skewer should meet brief resistance before sliding through cleanly — the flesh is tender but intact, not collapsing. If resistance remains, continue in 2-minute intervals, testing each time. Remove the pan from the heat the moment the flesh yields; carry-over cooking in the residual broth will complete any final softening.
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5
Allow the kabocha to rest in the broth off the heat for at least 10 minutes before serving; the flesh will continue to absorb the golden seasoning as it cools slightly. The pieces are ready to plate when they are suffused with the amber colour of the broth and carry a lacquered sheen. Arrange skin-side up or with the flat presentation edge downward. Spoon a little broth over each portion and garnish, if using, with a sprig of mitsuba or a strip of yuzu zest.