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1
Rinse the salt-packed anchovies thoroughly under cold running water. Separate them into fillets, removing the backbone. Set aside on a small plate. They should smell clean and briny, not sharp or fermented.
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2
Warm the olive oil in a wide, heavy pan over the lowest possible heat. Add the thinly sliced white onions and a pinch of salt. Cook slowly, stirring every five minutes, for 20 minutes. The onions should be fully softened and translucent but not yet coloured.
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3
Pour in the white wine. Continue cooking over low heat for a further 20–25 minutes, stirring occasionally, until the onions are deep gold, almost paste-like, and have almost entirely dissolved into the oil. This is where the dish lives or dies: pale or firm onions produce a different sauce entirely — 45 minutes is the minimum; no shortcut recovers the sweetness lost to haste.
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4
Remove the pan from the heat. Lay the anchovy fillets across the surface of the hot onions. Leave undisturbed for 2–3 minutes, then stir gently. The residual heat dissolves the anchovies completely into the onion mass. The sauce should be cohesive, glossy, and carry no visible anchovy pieces.
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5
Cook the bigoli in abundant well-salted boiling water. Because of their thickness and density, bigoli require longer than standard pasta — test at the time indicated on the packet and continue until the strand offers firm resistance at the centre but the outer surface is fully cooked. Drain, reserving a ladleful of pasta water.
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6
Transfer the bigoli directly into the pan with the onion-anchovy sauce. Toss vigorously over very low heat for no more than one minute, adding a splash of pasta water if the sauce tightens. The sauce should coat every strand; the rough surface of the bigoli will hold it. Serve immediately — the sauce cools rapidly and does not wait.