Fillet the fish, set aside the trimmings and remove any small bones from the fillets with tweezers. Set the fillets aside to be added to the soup later.
To make the stock, roughly chop the fish trimmings into three parts. Heat a large, heavy-based saucepan over a medium heat, and add the olive oil.
Add the fish trimmings and fry for 5-10 minutes until they begin to brown. Remove the fish trimmings from the pan and set aside on a plate.
Add the shallot, fennel, tomatoes, garlic, thyme, bay leaves, saffron and star anise. Fry gently over a medium heat for a few minutes, stirring regularly, until the vegetables have softened.
Add the cooked fish trimmings back into the pan, and pour in the boiling water. Bring back to a simmer and remove any scum that forms on the surface with a ladle or spoon. Reduce the heat and simmer gently for 35 minutes.
Place a sieve in a colander placed over a large saucepan. Ladle the stock into the sieve, then gently pour in any remaining liquid from the pan - taking care not to tip the fish or vegetables into the sieve. Season to taste with salt and freshly ground black pepper.
For the soup, place the potatoes into the fish stock. Bring to the boil and cook for 6-8 minutes, or until the potatoes are nearly cooked.
Cut the fish fillets into 5cm/2in pieces. Discard any mussels that are open or that don't close when tapped, or have broken shells.
Add the prawns, mussels and white fish to the saucepan and simmer for 2-3 minutes, or until the fish is cooked through and the mussels have opened. Discard any mussels that have not opened during cooking. Season to taste with salt and freshly ground black pepper.
To serve, ladle the fish soup into soup bowls, scatter with parsley, drizzle with olive oil and serve immediately.