Rinse the fish, pat dry, cut into fillets and remove bones. Cut fillets into bite-sized pieces. Rinse prawns, remove the heads, peel up to the tail segment and devein. Fry the fish frames (gilled) briefly in a hot pot in 1 tablespoon oil with the prawn shells. Add 1 liter (approximately 4 cups) of cold water to cover and bring to a boil with the star anise, bay leaf and thyme. Cook over low heat for about 20 minutes, just below the boiling point. Skim foam as needed.
Rinse the leek, onion, tomatoes, fennel, potatoes, carrot and garlic. Scrub or peel vegetables as necessary. Cut leek into rings. Cut potatoes into pieces. Core tomatoes and cut into pieces. Cut fennel, onion and carrot into thin strips. Cut the garlic into thin slices.
Pour the remaining oil in a hot pan and sauté the leek with the onion, fennel, carrot and garlic until translucent. Stir in tomato paste and paprika and deglaze with the white wine. Pour the fish stock through a fine sieve into the pot and bring to a boil. Add the potatoes and tomatoes, season with salt and pepper, add saffron and simmer for about 20 minutes. As needed, add water.
Scrub and debeard the mussels. Add to the soup along with the pieces of fish and prawns and cook until done over low heat. Do not allow to boil. Season with vermouth, salt and pepper.
If desired, serve with toasted bread and rouille.