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1
Peel the zucca gialla and cut into slices 8–10 mm thick. Slices thinner than this will disintegrate in the oil. Pat the cut surfaces dry.
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2
Heat the olive oil in a deep, heavy pan to 175 °C. Fry the squash slices in batches, turning once, until golden brown on both sides. This is where the dish lives or dies: pale, under-fried squash carries insufficient natural sweetness for the agrodolce balance to work — the colour must be a deep, even gold before the slices are lifted from the oil.
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3
Transfer the fried slices directly to a colander set over a bowl. While the squash is still hot, combine the white wine vinegar, sugar, fresh mint, and crushed garlic, then pour the raw agrodolce mixture over the squash in the colander. The heat of the slices begins the absorption immediately.
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4
Transfer the dressed slices to a serving dish, layering them as they come. Leave uncovered at room temperature for a minimum of 1 hour. The squash must cool completely while absorbing the marinade; it is ready when the surfaces are no longer glossy with free liquid and the slices yield easily to a fork.
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5
Scatter fresh mint leaves over the dish at service. The correct serving temperature is room temperature — not hot, not refrigerator-cold. Taste for balance between sweet and sour before bringing to the table.