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1
Place the baccalà pieces in a large bowl of cold water. Soak for 24–48 hours, changing the water every 8–12 hours. To judge readiness, taste a thin flake from the thickest piece: it should be mild and yielding, with residual savour but no aggressive salt.
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2
Drain the baccalà and pat every surface completely dry with kitchen paper. Moisture remaining on the surface will cause the fish to steam rather than sear in the pan.
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3
Submerge the dried peppers in warm water for 20 minutes. Lift them out, reserving the soaking liquid. Remove stems and seeds, then cut the flesh into strips. Taste the soaking liquid: it should be sweet-smoky and concentrated; set it aside.
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4
Warm the olive oil in a wide, heavy pan over a medium-high flame. Lay in the baccalà pieces without crowding. Brown briefly on each side until the surface is golden and lightly crusted — this is where the dish lives or dies: the sear seals sweetness into the fish and builds the base flavour the braise will later carry.
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5
Remove the baccalà to a plate. In the same pan over a medium flame, add the rehydrated pepper strips, olives, and capers. Stir for one minute until fragrant, then add the crushed tomato and 2 tablespoons of the reserved pepper soaking liquid. Stir to combine. The sauce should smell sweet, smoky, and sharp in equal measure.
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6
Return the baccalà to the pan, nestling the pieces into the sauce. Reduce the heat to low, cover, and braise for 20–25 minutes. The dish is done when the baccalà yields completely to gentle pressure from a spoon and the sauce has unified around it into a single, cohesive body — no raw tomato acidity remaining.