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1
Begin 5 to 7 days before serving. Place the dried stockfish in a large container under cold running water, or submerge fully and change the water at least once daily. After 4 to 5 days the soaking water will turn milky and slightly viscous from dissolved proteins; reserve one cup of this liquid for the braise. Soaking is complete when the fish is fully supple, ivory throughout, and yields to moderate finger pressure.
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2
Drain the rehydrated stockfish and cut into large pieces — no smaller than 6 to 7 cm — to prevent disintegration during braising. The fish will carry a pronounced fermented aroma at this stage; this is correct and will mellow entirely in the pot.
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3
Warm the olive oil in a Provençal earthenware daubière or heavy wide casserole over a moderate flame. Add the sliced onions and cook, stirring occasionally, until they are soft, translucent, and beginning to colour at the edges — the sign that the base is ready to receive the tomatoes.
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4
Add the crushed tomatoes, red and green pepper strips, unpeeled garlic cloves, and bouquet garni. Stir to combine, then lay the stockfish pieces over the vegetables in a single layer. Pour over the reserved cup of soaking liquid. This is the step on which the dish lives or dies: the fish must be large enough to hold its shape, the heat low enough that the liquid barely trembles, and the lid on — a vigorous boil will destroy the stockfish's gelatinous texture and scatter the sauce before the flavours have had time to fuse. Braise gently for 45 minutes.
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5
After 45 minutes, tuck the large potato chunks into the braise among the fish pieces, and add the Niçois olives. Replace the lid and continue braising for a further 45 minutes. The potatoes are done — and the dish is ready — when their edges have begun to break apart, dissolving into the rust-coloured broth and thickening it visibly. A waxy potato that holds a clean edge signals undercooking.
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6
Remove the bouquet garni. Taste the broth: it should be round, deeply savoury, and carry the integrated funk of the stockfish rather than any raw or sharp note. Ladle into wide, shallow bowls, ensuring each portion receives fish, potato, peppers, olives, and plenty of broth. Serve with aïoli and crusty bread.