How to Make Bouillabaisse
Start the Rouille
Simmer a peeled and cubed baking potato in salted saffron water until tender. Let the potato cool completely.
Finish the Rouille
In a blender, pulse the potato and its saffron cooking water with cayenne, garlic and egg yolks, then blend in olive oil until the rouille is smooth and creamy.
Prep the Fish Bones
To start the base for the bouillabaisse, thoroughly rinse fish bones and heads in cold water in a colander set in the sink.
Cook the Aromatics
Cook onions, celery, fennel and leek with saffron and cayenne until softened; add the fish bones and heads, shrimp shells and an herb-and-spice sachet.
Simmer the Broth
Add enough water to just cover the fish bones and cook for 20 minutes, skimming off the foam as it rises to the surface.
Finish the Broth
Add quartered ripe plum tomatoes to the pot and cook gently for another 30 minutes. Pick out and discard the herb-and-spice sachet and any large fish bones.
Puree the Soup
Ladle the broth—fish bones and all!—into the blender and puree until smooth. Strain the soup through a fine sieve, pressing on the solids.
Add the Fish
Return the soup to a clean casserole and bring to a simmer. Add cooked potatoes and seasoned fish fillets.
Finish the Bouillabaisse
When the fish fillets are partially cooked, add the shrimp and mussels and simmer until cooked through. Serve with the garlicky rouille and crusty bread.