Put the salt cod in a bowl, cover with plenty of cold water and leave to soak for 1–2 days, changing the water twice daily. Drain the cod and cut into small chunks, discarding any skin and bones.
Heat the oil in a large saucepan and gently fry the onion for 5 minutes until softened. Add the garlic and cook for 1 minute. Add the stock and crumble in the saffron. Bring to the boil, then reduce the heat to a gentle simmer.
Add the salt cod and potatoes and cover with a lid. Cook gently for about 20 minutes until the fish and potatoes are very tender.
Stir in the tomatoes and parsley and then cook for 5 minutes until the tomatoes have softened. Season to taste (you might not need any salt, depending on the saltiness of the fish). Ladle into shallow bowls and serve with warm bread.