Heat the oil in a large, heavy-based saucepan over a medium-low heat, add the onion and garlic and cook gently for 8–10 minutes or until softened.
Stir in the paprika and saffron and cook for a further minute. Stir in the fish, then pour over the Madeira. Add the stock, tomato purée, tomatoes and bay leaves and season with salt and pepper. Bring to the boil, then reduce the heat and simmer gently for 5 minutes.
Stir in the live mussels, cover and cook over a low heat for about 3 minutes or until they have opened. Discard any that remain closed. Alternatively, if using cooked shelled mussels, simmer the stew for 2–3 minutes more, or until the fish is cooked and tender, then stir in the cooked mussels. Cook for 30 seconds or until the mussels are heated through and piping hot.
Ladle into bowls and sprinkle with the parsley. Serve immediately with crusty bread.