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1
Heat the oil in a wide, heavy pot over medium-low heat. Add the grated onion paste first; it will spit and reduce quickly. Add the sliced onions. Cook, stirring regularly, for 30–45 minutes, reducing heat as needed to prevent burning. The onions are ready when they are a deep amber-brown, fully collapsed, and smell of concentrated sweetness — no trace of raw pungency should remain.
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2
Raise the heat to medium-high. Add the meat in a single layer and brown on all sides — do not crowd the pan. The surface should develop a dark, sealed crust with clear Maillard colour before the meat is turned.
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3
Add the carrot chunks and stir to coat. Pour in the water or stock and bring to a gentle simmer. Skim any foam that rises. Simmer uncovered for 20 minutes, until the carrot begins to yield at its edges when pressed with a spoon.
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4
Add the drained potato chunks. Continue simmering for 12–15 minutes only, until a skewer meets moderate resistance at the centre — the potato must be cooked through but intact; it should not begin to cloud the broth or crumble at the edges.
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5
Remove the pot fully from the heat. Allow the liquid to cease bubbling. Break the roux blocks into the still liquid and stir steadily until each piece has fully dissolved — the sauce will thicken noticeably within 2–3 minutes of stirring. No lumps should remain visible; the surface should be uniformly dark and glossy.
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6
Return the pot to low heat. Stir in the grated apple and honey. Add the dark chocolate. Simmer gently for a further 10 minutes, stirring occasionally. The sauce is done when it coats the back of a spoon heavily and the raw edge of apple sweetness has rounded into the background — the finish should be mild, warming, and faintly fruity.
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7
Remove from heat, cool, and refrigerate overnight. Reheat gently the following day, stirring from the base of the pot. The sauce will have thickened further and darkened; the spice and vegetable elements will have integrated fully. Serve over Japanese short-grain rice.