True baccalà alla vicentina begins long before you light the stove — with dried stockfish that must soak in cold water for at least two to three days, sometimes longer if it is very hard and woody. Place it in a large basin, skin side up, and change the water at least twice a day, keeping the basin in a cool spot or the refrigerator so nothing turns. You will see it soften and swell as it rehydrates, and the strong sea smell will mellow considerably. This patience is not optional; it is what transforms a plank-hard fish into something you can bone, flake, and simmer into velvet. If you can find stockfish already soaked and cleaned at an Italian fishmonger, you may skip ahead, but do taste a small piece first to judge how much toughness remains.

Once softened, lift the stockfish from its water and lay it on a board to clean properly. Pull away the skin in strips, working slowly with your fingers so you keep the flesh intact, and run your hands through the fillets to find and remove every fine bone, because stockfish hides many. Cut the cleaned fish into pieces about the size of your palm, keeping the pieces roughly even so they cook at the same pace. Pat them dry with a clean cloth, then dust each piece lightly in flour — this thin coating helps the fish hold together as it simmers for hours and gives the final sauce a touch of body.

In a heavy pot, ideally an old terracotta or enameled cast-iron one that holds heat gently and evenly, warm half the olive oil over low heat. Add the thinly sliced onions and let them cook slowly, stirring now and then, until they turn soft and translucent but never brown — twenty minutes of patience here pays back tenfold in the final dish. Stir in the chopped anchovy fillets and minced garlic, pressing the anchovies with your spoon until they melt into the onions and disappear, leaving behind only their deep savoury perfume. This soffritto is the backbone of the whole dish, so do not rush it or raise the heat to hurry it along.

Remove half the onion mixture and set it aside for a moment. Arrange half the floured fish pieces over the onions left in the pot, then scatter over the grated cheese, a little chopped parsley, and a good grinding of black pepper. Repeat with the remaining onions, fish, cheese, and parsley, finishing with a final layer of onions on top. Pour over the remaining olive oil in a slow, steady stream, letting it settle down between the layers, then pour in the milk until it comes just level with the fish, adding a touch more if needed so nothing peeks out dry.

Bring the pot to the barest whisper of a simmer, then lower the heat as far as it will go — you want only the occasional lazy bubble breaking the surface, never a boil, or the fish will turn stringy and the sauce will split. Cover partially and let it cook this way for three to four hours, checking in only every twenty minutes or so to give the pot the gentlest shake or a single careful pass with a wooden spoon around the edges. This is the old Vicentine trick: you disturb it as little as possible, letting time and low heat do the work of binding milk and oil into a creamy sauce, rather than vigorous stirring, which would break the delicate fish into shreds.

As the hours pass, you will notice the liquid around the fish thickening and turning pale golden, almost like a light custard, as the fish's natural gelatin, the melted cheese, and the oil slowly come together. Taste the sauce near the three-hour mark and adjust the salt carefully, remembering that both the anchovies and the cheese already carry good salinity. If the sauce still looks thin and separated, let it continue over the lowest heat rather than raising the temperature, since only time will coax it into the right creamy consistency.

When the fish is fork-tender and the sauce has turned rich and unified, take the pot off the heat and let it rest, covered, for ten to fifteen minutes. This short pause allows the sauce to settle and thicken just slightly more, and makes it far easier to lift out neat pieces of fish without them falling apart. Nonna Fiore always said a dish this patient deserves one last moment of patience before it reaches the table.

While the baccalà rests, bring salted water to a boil and whisk in coarse cornmeal in a thin, steady stream, stirring constantly to avoid lumps. Lower the heat and let the polenta cook gently for about forty minutes, stirring often, until it turns thick, smooth, and pourable rather than stiff. In Veneto, this dish is always paired with polenta soft enough to spread like a pillow beneath the fish, not the firm, sliceable kind.

Spoon a generous pool of soft polenta onto each warmed plate and top it with a piece or two of the baccalà, letting plenty of its creamy sauce run down over the cornmeal. Finish with a light scattering of fresh parsley and, if you like, a final thread of good olive oil. Serve at once, while the polenta is steaming and the sauce is at its silkiest, just as it has been served at Veneto tables for generations.