1. In a pot, soften the sliced leek and the sliced onion in olive oil.
2. Pour in the white wine and enough water to make a soup, season with salt and pepper and bring to the boil.
3. Add the cod and fish fillet cut into large pieces and cook gently for about 10 minutes, just until done, then lift the fish out carefully and keep warm.
4. For the aioli, work the egg yolks with the crushed garlic, then whisk in the olive oil in a thin stream into a thick, mayonnaise-like cream.
5. Stir half the aioli little by little into the hot (but not boiling) fish broth, stirring constantly, until the soup thickens silkily (do not let it boil again!).
6. Serve the thickened soup with the fish, offering toast spread with the remaining aioli.
Tip: Bourride is the white, creamier sibling of bouillabaisse – here the aioli is not just an accompaniment but also thickens the soup. Take care that the soup does not boil after adding the egg-based aioli, or it will split.
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