Peel the onions and slice them as thinly and evenly as you can manage, ideally with a sharp knife or a mandoline. The thinness matters more than you might think: it is what allows the onions to break down into a soft, almost jam-like base rather than staying in distinct rings. Set them aside in a bowl while you warm the oil, and try not to rush this part — a good bigoli in salsa begins with patient knife work.

Warm the olive oil in a wide, heavy-bottomed pan over the lowest heat your stove allows. Add the sliced onions, a small pinch of salt, and stir to coat them in the oil, then cover the pan with a lid. Let them cook gently for 35 to 45 minutes, stirring occasionally and adding a splash of water if they begin to catch. You are not looking for colour or caramelisation here — the goal is onions that have collapsed into a pale, tender, almost translucent mass, sweet rather than sharp. This slow sweating is the heart of the dish, and no amount of high heat can shortcut it honestly.

Once the onions are completely soft, add the anchovy fillets directly to the pan along with the optional splash of white wine. Turn the heat down further if needed and use a wooden spoon to press and stir the anchovies until they dissolve entirely into the onions, disappearing into the sauce rather than remaining as visible pieces. Let everything simmer together gently for another 5 to 10 minutes, until the sauce turns a deep golden-amber colour and smells rich and savoury rather than fishy. Taste before adding any extra salt, since the anchovies bring plenty on their own.

Bring a large pot of water to a rolling boil and salt it generously, remembering that bigoli is a dense, thick pasta that benefits from plenty of room to move. Cook according to the package instructions, usually 9 to 12 minutes, until al dente, stirring occasionally to keep the thick strands from sticking to one another or to the bottom of the pot. Just before draining, scoop out a cup of the starchy cooking water and set it aside — it will help bind the sauce to the pasta in the final step.

Drain the bigoli, letting a little water cling to the strands, and add it directly to the pan with the onion and anchovy sauce. Toss over low heat for one to two minutes, adding splashes of the reserved pasta water as needed until the sauce clings glossily to every strand rather than pooling at the bottom of the pan. The pasta should look well coated but not swimming in liquid.

Divide the bigoli among warmed plates, spooning any extra sauce from the pan over the top. Finish with a generous crack of black pepper and, if you like, a final thread of good olive oil. Serve at once, while the strands are still glossy and warm, and resist any temptation to reach for the cheese — in this house, and in Venice, fish and formaggio simply do not share a plate.