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1
Place the lamb pieces in a wide, heavy braising pan with the garlic and rosemary. Pour over the white wine. Braise over a moderate flame, turning the pieces occasionally, until the lamb is cooked through and the wine has reduced to a concentrated braising liquor. The meat is done when it offers no resistance to a skewer and the liquor has reduced to a few spoonfuls of fragrant, glossy liquid.
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2
Remove the pan entirely from the heat. Allow thirty seconds for the pan to cool slightly — this gives the critical safety margin against scrambling. Meanwhile, whisk the egg yolks and finely grated Pecorino together in a bowl until fully combined and smooth; the mixture must be homogeneous before it meets the pan.
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3
Tilt the pan and pour the liaison in slowly, stirring constantly so that the mixture meets the hot braising liquor in a thin, even stream. Work continuously, coating every piece of lamb. This is where the dish lives or dies: the residual heat of the lamb and pan is sufficient to thicken the eggs into a custardy, clinging sauce — any direct flame will produce scrambled egg chunks rather than a creamy liaison. The sauce is done when it coats the lamb in a smooth, pale, just-set layer that moves slowly when the pan is tilted.