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1
Soak the stockfish in cold water for 3–4 days, changing the water daily; baccalà requires 48–72 hours. Once fully rehydrated and desalted, remove all skin and bones and cut the flesh into sections of roughly equal size. The fish should be pliable and yielding to the touch — any remaining rigidity means further soaking is required.
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2
Soak the dried porcini in warm water for 20–30 minutes. Lift the mushrooms out, squeeze gently, and chop coarsely. Pass the soaking liquid through a cloth or fine sieve to remove all grit; reserve this liquid for the braise.
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3
Warm the olive oil in a wide, heavy pan over low heat. Add the onion and cook slowly until soft and translucent. Add the garlic and the anchovy fillets and continue to cook, pressing the anchovies against the base of the pan, until they dissolve entirely into the oil and the soffritto smells deeply savoury and unified — no trace of raw onion or visible anchovy remains. This is the umami backbone of the dish; without it the buridda is flat.
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4
Add the white wine and raise the heat briefly to let the alcohol cook off. Add the soaked porcini, the strained porcini liquid, the capers, and half the olives. Stir to combine. The liquid should be a dark, aromatic broth — earthy, briny, and savoury.
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5
Lay the prepared fish sections into the pan in a single layer. Add the pine nuts whole. Cover and braise gently over low heat for 20–25 minutes. The fish is done when it is tender and yielding but still holds its form as identifiable sections — it must not be falling apart or beginning to shred.
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6
In the final 5 minutes, add the reserved olives. This preserves their texture and fruity character. Taste the sauce for salt — the anchovy, capers, and olives carry considerable salinity, and further seasoning is rarely needed. The sauce should be complex and deeply savoury, with a perceptible fruitiness from the olives.
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7
Serve directly from the pan with polenta or toasted bread alongside to absorb the sauce.