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1
Heat the olive oil in a wide, heavy-based pot over high heat. Add the lamb pieces in a single layer — do not crowd them. Brown on all sides until deeply coloured, turning as needed. The crust should be mahogany, not pale gold; under-browned lamb produces a flat-tasting braise.
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2
Reduce the heat to medium. Add the sliced onion, sweet pepper strips, and the optional peperoncino. Cook, stirring occasionally, for 5 minutes, until the onion has softened and the peppers have begun to wilt.
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3
Pour in the white wine and raise the heat. Allow it to reduce by half — the raw alcohol smell will have left the pot, replaced by a softer, fruit-forward vapour.
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4
Add water to just cover the lamb. Bring to a gentle simmer, cover, and braise over low heat for 1 to 1½ hours, until the lamb is completely tender — the meat should yield at the touch of a spoon and begin to pull from the bone.
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5
Remove the pot from the heat and allow the violent bubbling to subside entirely. In a bowl, beat the eggs thoroughly with the lemon juice (or white wine vinegar) and the chopped parsley. Pour the liaison into the braising liquid in a slow, steady stream, stirring constantly. This is where the dish lives or dies: the liquid must be hot enough to cook the egg to a silky, thickened sauce, but it must not be boiling — boiling liquid scrambles the egg rather than binding it. The sauce will turn slightly golden and coat the back of a spoon.
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6
Serve immediately, ladling the lamb, peppers, and sauce into warmed bowls. The sauce should be fluid but clearly thickened, with a bright, acidic finish that cuts the richness of the lamb.