1 Scale and gut the fish, then rinse thoroughly under running water and pat dry.
2 Slice the hake and gurnard. Remove the fillets from the other fish. Set aside.
3 In a large pot, pour 3 tablespoons of olive oil. Add the sliced onions, finely chopped garlic and leeks. Let the vegetables stew, covered, for 15 minutes, stirring often.
4 Add the fish trimmings, broken bones and bouquet garni. Stir constantly until the bones turn white. Pour in the white wine and 1 litre (1.1 qt) of water. Add the tomato paste, season with salt and pepper. Bring the stock to a boil and let it simmer for 1 hour, covered, skimming off the foam that rises regularly.
5 In the meantime, wash, scrape and drain the mussels. Place them in a pot over high heat and stir them until they open. Drain them, reserving their liquid.
6 Strain the stock through a sieve. Press the remains through a food mill and pour into the stock along with the mussel liquid. Bring the stock back to a gentle simmer.
7 Mix the egg yolks and crème fraîche in a bowl. Pour a ladle of stock over it, stirring constantly. Add this mixture to the stock, stirring constantly with a whisk. Place the fish fillets and steaks, mussels and langoustines in a thick-bottomed pot. Pour the stock gently over everything and return the royal fish soup to heat on very low heat for 10 minutes.
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