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Heat a large pot over high heat.
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Add 1 tablespoon olive oil and heat.
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Add the chorizo and cook until some of the fat is rendered and the chorizo starts to brown.
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Add the onions, garlic, fennel, and red pepper flakes and cook until the onions begin to brown, about 6 to 7 minutes.
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Add the bay leaves and thyme, and season with salt and pepper.
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Deglaze with the white wine.
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Cook, scraping the bottom of the pot, until the wine is reduced by 1/4, about 10 minutes.
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Break up the tomatoes with your hands into the pot.
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Add tomatoes and juices and the fish stock.
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Bring to a boil.
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Reduce the heat to a simmer and cook for 15 minutes.
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Return to high heat and add the lobsters and crabs, cover, and cook for 5 minutes.
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Add the clams and mussels, cover, and cook for another 5 minutes.
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Add the squid, oysters, and shrimp, cover and cook another 5 minutes, or until all of the shellfish open and the shrimp are cooked through.
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Add the parsley and season with salt and pepper, to taste.
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Spread the aioli on toasted French bread slices and serve with the soup.
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2 egg yolks*
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1 clove garlic
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1/2 lemon, juiced
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1/2 cup basil leaves
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Pinch cayenne
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Salt and freshly ground pepper
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1 1/2 cups olive oil
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In a food processor, combine egg yolks, garlic, lemon juice, basil, cayenne, salt and pepper.
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Puree until smooth.
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With the machine running, slowly add the olive oil until the mixture is thick and emulsified.
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Thin with a little more lemon juice, if necessary.
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*RAW EGG WARNING
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Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness.
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To reduce this risk, we recommend you use only fresh, properly-refrigerated, clean, grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the shell.