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1
Place the lamb pieces in a wide, heavy pan with the white wine, water, garlic, and bay leaves. Bring to a gentle simmer over medium heat and braise, partially covered, until the meat is completely tender and the cooking juices are clear and lightly reduced. The flesh should yield without resistance when pressed.
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2
Beat the eggs, grated Pecorino, and lemon juice together in a bowl until fully combined. Adding the lemon juice first — before the eggs meet any heat — slightly denatures the egg proteins and stabilises the subsequent emulsification.
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3
Remove the bay leaves and garlic. Reduce the cooking juices if necessary so they remain concentrated but plentiful. Take the pan off direct heat and allow the liquid to fall to approximately 80 °C — hot but no longer simmering. This is where the dish lives or dies: if the juices are boiling when the egg mixture enters, the brodetto scrambles instantly rather than emulsifying into a creamy sauce.
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4
Pour the egg-Pecorino-lemon mixture into the hot cooking juices in a slow, steady stream, stirring constantly. Continue stirring without pause, moving a wooden spoon through the entire pan, until the sauce thickens to a consistency that coats the back of the spoon in a creamy, uniform layer.
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5
Scatter the fresh marjoram over the pan. Serve immediately in warmed deep plates with rustic bread. The brodetto does not reheat successfully; it must reach the table at once.