How to Make It
In a medium saucepan, combine the potato, saffron, a pinch of salt and 2 cups of water. Bring to a boil and cook until the saffron water is reduced by half and the potato is cooked through, about 20 minutes. Cool completely, then transfer the potato and saffron water to a blender. Add all of the remaining ingredients except the oil and pulse to combine. With the machine on, slowly drizzle in the oil until well blended. Season with salt. Transfer to a serving bowl; refrigerate.
Assemble all of the ingredients on a piece of cheesecloth, wrap into a bundle and tie with kitchen string.
Rinse all of the fish heads and bones until the water runs clear. Cut the fillets into 2-inch pieces and transfer them to a bowl; cover and refrigerate.
In a large enameled cast-iron casserole or pot, heat the olive oil. Add the onions, celery, fennel, leek, saffron and cayenne and cook over moderate heat until the vegetables soften, 8 minutes. Add the pastis and cook until evaporated. Add the tomato paste and cook, stirring, until beginning to caramelize, about 5 minutes.
Add the fish heads and bones, shrimp shells, herb-and-spice sachet and enough water to just cover, about 16 cups. Bring to a simmer and cook over moderately low heat for 20 minutes, skimming off the foam that rises to the surface. Stir in the tomatoes and cook gently for 30 minutes.
Meanwhile, cook the potatoes in a large saucepan of salted boiling water until tender, about 15 minutes. Drain well.
Pick out and discard the herb-and-spice sachet and any large fish bones. Working in batches, transfer the contents of the casserole to a blender and puree until smooth. Strain the soup through a fine-mesh sieve into a clean pot, pressing on the solids.
Bring the soup to a simmer. Add the potatoes. Season the fish with salt and pepper and add to the soup. Cook over low heat for 3 minutes. Add the shrimp and mussels, cover and cook until the mussels open and the fish and shrimp are cooked through, 2 minutes longer. Season with salt, pepper and cayenne.
Stir 2 tablespoons of the hot soup into the rouille. Ladle the bouillabaisse into shallow bowls. Serve with the rouille and crusty bread.