Drain the soaked stockfish and pat it dry. Pull out any loose bones and cut it into 6 cm / 2.5-inch pieces, keeping the skin on. Peel the potatoes and cut them into 3 cm / 1.25-inch chunks, then rinse the capers under cold water for 2 minutes.
Heat the olive oil in a 28 cm / 11-inch Dutch oven over medium heat. Add the onion and celery with a pinch of salt and cook for 8 minutes, stirring, until soft and pale gold. This is your soffritto. Stir in the garlic and pine nuts for 1 minute until fragrant.
Pour in the wine and boil for 2 minutes. Add the crushed tomatoes, olives, capers and raisins, then simmer for 10 minutes until the sauce is thick enough to leave a trail when you drag a spoon through it.
Nestle the stockfish into the sauce and tuck the potatoes around it. Add the hot water so the liquid comes just below the top of the potatoes. Bring to a bare simmer, cover, and cook on low heat for 40 minutes. Keep the bubbles lazy, because a hard boil makes the fish stringy and breaks the potatoes. Shake the pot gently once or twice instead of stirring.
Take off the lid and cook for 9 minutes more, until the sauce is glossy and clings to the fish and a fork flakes a piece with light pressure. Taste, add the remaining salt and the pepper, then scatter with parsley and serve hot.