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1
Soak the stale bread in cold water for 10 minutes. Lift it out and squeeze it with both hands, working it thoroughly until no further water can be extracted. The bread must be as dry as possible — residual moisture is what causes the pallotte to collapse in the oil.
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2
Combine the squeezed bread, beaten eggs, very finely grated Pecorino, chopped parsley and black pepper in a bowl. Work the mixture with the hands until it is fully cohesive and uniform, with no visible pockets of cheese or unincorporated bread. Chill for 10 minutes if the mixture feels slack.
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3
Roll the mixture into balls the size of walnuts, pressing firmly so they are compact and smooth. Set them on a tray in a single layer.
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4
Heat the olive oil for shallow-frying in a wide, heavy pan over medium-high heat until it shimmers visibly and a breadcrumb dropped in sizzles immediately. This is where the dish lives or dies: oil that is not hot enough causes the pallotte to absorb fat and turn greasy rather than forming the structural crust they need to survive the subsequent simmering. Fry the pallotte in batches, turning them to colour on all sides, until the exterior is an even deep gold. Lift out and drain on a rack.
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5
In a separate wide pan, warm the olive oil for the sauce over medium heat and sweat the soffritto — onion, celery and carrot — until softened and translucent, with no colour. Add the passata and torn basil. Cook uncovered, stirring occasionally, until the sauce reduces to a dense, coating consistency. A thin sauce will not penetrate and flavour the pallotte adequately.
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6
Lower the fried pallotte into the sauce in a single layer. Simmer over the lowest possible heat for 30 minutes, partially covered, turning the pallotte once at the halfway point. The heat must remain gentle throughout — aggressive simmering will break them apart. The pallotte are done when they have swelled slightly, their interiors are tender when pressed lightly with a spoon, and they have drawn the sauce into themselves.
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7
Serve as a primo or secondo with toasted bread alongside to absorb the remaining sauce.