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1
Pour the day-old minestrone into a heavy pot — earthenware if available — and set over a moderate flame, bringing it slowly back to a simmer and stirring occasionally, so the heat rises evenly through the dense, settled soup rather than scorching the starchy solids against the base. The soup should loosen as it warms; a steady, gentle bubble is correct.
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2
Add the torn cavolo nero to the simmering pot, pressing the leaves beneath the surface so they cook in the broth rather than steaming above it, which keeps their mineral bitterness from staying sharp and raw. Cook until the leaves are completely tender and dark, offering no resistance when pressed between two fingers — that bitterness should have passed fully into the broth, rounding and deepening it.
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3
Crumble the stale pane sciocco into the pot in stages, stirring well after each addition so each batch is absorbed before the next goes in — this is where the dish lives or dies, because bread added all at once seizes into dense, unworkable clots that no amount of stirring will recover. Continue to cook, stirring steadily, until the bread has fully broken down and the soup has thickened to barely pourable; it should hold a brief shape in the bowl and no loose broth should pool at the surface.
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4
Ladle into wide, deep bowls and pour the raw olive oil in a generous spiral over the surface of each bowl, so it sits in the furrows of the thick soup rather than disappearing into it — it functions here as the sauce, and its raw, grassy sharpness is what lifts the whole dish. Serve immediately.