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1
Dry each rabbit piece thoroughly with a cloth or paper. Season well with salt and black pepper on all sides. Heat the olive oil in a wide, heavy braising pan over high heat. Brown the rabbit in batches — do not crowd the pan. Each piece must develop a deep golden crust on all sides before it is turned. The pan should sizzle loudly; if it steams, the temperature has fallen too low. The dish is done at this stage when each piece is firmly crusted and a rich brown fond has built on the pan floor.
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2
Return all the browned rabbit pieces to the pan. Pour in the white wine. Allow it to bubble hard, scraping up the fond, and reduce by half. The sharp alcohol smell will soften and the wine will take on a rounded, slightly sweet character — that change of smell marks the point at which to proceed.
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3
Add the Gaeta olives, the rosemary sprig, the whole garlic cloves, and the dried chilli. Stir once to distribute. Cover the pan, reduce the heat to low, and braise for 40–50 minutes. Lift the lid occasionally: the rabbit is ready when the thigh meat yields to gentle pressure with a finger and begins to pull away from the bone.
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4
Remove the lid. Add a splash of white wine vinegar. Raise the heat to medium and cook uncovered for a further 10 minutes, turning the rabbit in the sauce. The sauce is done when it has reduced to a glossy consistency that coats and clings to the pieces rather than pooling in the pan — confirmed by sight.
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5
Remove the rosemary sprig and the dried chilli. Taste for salt. Serve directly from the pan, accompanied by crusty bread or polenta bianca for mopping the olive-rosemary sauce.