Rinse the salt cod under cold water. Put it in a 4-liter / 4-quart bowl, cover with cold water, and refrigerate for 24 hours, changing the water at least 4 times. Tear a small flake from the thickest piece and taste it. It should taste lightly seasoned, not sharply salty. If it's still harsh, soak it 6 to 12 hours more.
Drain the cod and pat it dry. Peel off the skin, pull out any bones, and cut the fish into about 8 pieces, roughly 6 cm / 2.5 inches each. Finely dice the onion and celery and slice the garlic.
Warm the olive oil in a 28 cm / 11-inch deep sauté pan with a lid over medium-low heat. Add the onion and celery and cook for 6 minutes, stirring now and then, until soft and pale with no browning. Add the garlic and chili flakes and cook for 1 minute until fragrant.
Pour in the wine and simmer for 2 minutes until the sharp smell cooks off. Add the crushed tomatoes with their juice, the water, capers, and olives. Simmer gently for 8 minutes until the broth is slightly reduced and tastes bright and sweet. Don't add salt yet.
Nestle the cod pieces in a single layer in the broth and spoon some liquid over the tops. Cover and keep at a lazy simmer, with only small bubbles, for 8 to 10 minutes, until the thickest piece is opaque, reaches 145 F / 63 C, and flakes into large pieces. Don't stir. Shake the pan gently if you need to move the fish. Toast the bread while the cod simmers.
Taste the broth and add black pepper, plus a pinch of salt only if it needs it. Take the pan off the heat and scatter the parsley over. Ladle the cod and broth into shallow bowls and serve with the toasted bread.