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1
For the Aioli: Soak the breadcrumbs in 1 tablespoon of wine vinegar for 5 minutes, then squeeze the crumbs dry in the corner of a towel.
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2
In a food processor fitted with the metal blade, chop the garlic, then add crumbs and combine with garlic to make a smooth paste. Add egg yolks, and all the other ingredients except the oil and combine. Scrape down sides. Now, with the motor running, add olive oil in a slow, steady stream. When all the oil is in, you have aioli.
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3
In a 4- to 6-quart saucepan, bring the court bouillon ingredients to a boil, partially cover the pan, and cook over low heat for 30 minutes.
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4
Meanwhile, make the Aioli. Spoon 2/3 cup of Aioli into a small sauceboat and cover with plastic wrap. Put the rest of the sauce (about 1 1/3 cups) into a 3- to 4-quart saucepan.
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5
Strain the court bouillon through a sieve into a bowl, pressing down hard on the vegetables and trimmings with a spoon before discarding them. Wash the pan and return the court bouillon to it. Add the fish, bring to a boil and simmer uncovered for 3 to 8 minutes, or until the fish is just firm to the touch. Watch the fish CAREFULLY!! Different kinds and thicknesses cook at different speeds. With a slotted spoon or spatula, transfer the pieces to a heated platter as soon as they are done. Cover the platter loosely to keep the fish warm.
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6
Off the heat, beat the remaining 4 yolks, one at a time, into the aioli in the saucepan. Add 1 cup of hot fish broth, beating constantly, then gradually beat in the remaining broth. Cook over low heat, stirring, until the soup is thick enough to coat the whisk lightly. Do NOT let it come to a boil! Season with salt, pepper and lemon juice if needed.
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7
While the bouillon simmers also make the croutes. Preheat the oven to 325 degrees F. Spread the slices of bread in one layer on a baking sheet and bake for 15 minutes. With a pastry brush, lightly brush both sides of each slice with olive oil. Then turn slices over and bake for another 15 minutes, or until the bread is completely dry and lightly browned. Rub each slice with the cut garlic clove and set aside.
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8
To serve, pour the soup into a large tureen and bring it to the table with the platter of fish, a bowl of the sliced potatoes, the sauceboat of aioli and the croutes. Line the bottom of each soup bowl with potatoes and ladle in the soup. Pass the croutes and aioli to put on top. Eat at least part of the soup like this. Then, pass the platter of fish. Put some in your bowl and add some more broth, aioli and croutes. This is the second course of the meal.
