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1
Desalt the anchovies: submerge the whole fish in cold water for 30 minutes, changing the water once. Rinse, split along the spine, and remove all bones. Pat dry. They are ready when they smell clean and pleasantly briny, not harsh.
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2
Warm the olive oil in a wide, heavy pan over the lowest possible heat. Add the thinly sliced onions and a pinch of salt. Cook, stirring occasionally, for 45–60 minutes. The onions must collapse entirely into a pale golden, sweet mass with no remaining translucency. Taste: they should carry no raw sharpness. Pour in the white wine and allow it to reduce for a further 10 minutes.
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3
Add the anchovy fillets to the collapsed onion oil. This is where the dish lives or dies: stir constantly over low heat for 5–10 minutes until every piece of anchovy has dissolved completely into the sauce, leaving no visible trace of fish — only a unified, deeply savoury coating. The surface of the pan should show an amber-gold oil carrying the onion; no solid anchovy fragments remain.
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4
Bring a large pot of well-salted water to a rolling boil. Cook the bigoli until al dente — the rough surface will feel slightly resistant at the centre when pressed between the fingers.
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5
Reserve a ladleful of the starchy cooking water, then drain the bigoli. Transfer them directly to the pan of sauce over low heat. Toss vigorously, adding the pasta water a little at a time, until each strand is coated in a cohesive, silky sauce that does not pool at the bottom of the pan.