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1
Submerge the baccalà pieces, skin side up, in a deep vessel of cold water. Refrigerate for 48 hours, changing the water 3–4 times. At the end of soaking, press a piece: it should feel pliant and the flesh should give without stiffness. Taste a thread of the thinnest part — it must be saline but not aggressively salty.
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2
Place the dried Senise peppers in warm water and allow them to reconstitute fully. Drain and slice. The flesh should be supple and the colour a deep brick-red throughout.
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3
Pat the baccalà pieces dry. Dust lightly on both sides with plain flour, shaking off the excess. Heat the olive oil in a wide, heavy pan over a medium-high flame. Lay the pieces skin side down and fry undisturbed until golden; turn once and colour the flesh side. Remove and set aside. The skin should have crisped and the flour formed a pale gold crust on both sides.
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4
In the same oil, over a medium flame, add the sliced reconstituted peppers and fry briefly — they need only a short time; they should begin to colour at the edges and release a sweet, faintly smoky aroma into the pan.
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5
Add the estratto di pomodoro, black olives, capers, and crumbled peperoncino to the pan. Stir to combine and allow the tomato concentrate to darken slightly and fuse with the oil — this is the moment on which the dish lives or dies: the estratto must be cooked briefly in the fat until it deepens in colour and smells roasted and concentrated rather than raw, building the agro-salato-dolce base that defines the Lucano sauce.
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6
Return the baccalà pieces to the pan, skin side up. Add a small amount of water if the sauce is very thick. Cover, reduce the heat to a gentle simmer, and cook for 15–20 minutes. Do not stir; shake the pan occasionally if adjustment is needed. At 15 minutes, check: the sauce should have thickened and the skin of the baccalà should have softened and begun to gelatinise into the surrounding liquid. The baccalà must remain in intact pieces.
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7
Remove the lid and assess the sauce: it should coat a spoon and hold the impression of the baccalà pieces. The surface should be glossy with olive oil. Serve directly from the pan with dense Lucano bread alongside.