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Cook, scraping the bottom of the pot, until the wine is reduced by 1/4, about 10 minutes.
Break up the tomatoes with your hands into the pot.
Add tomatoes and juices and the fish stock. Bring to a boil. Reduce the heat to a simmer and cook for 15 minutes. Return to high heat and add the lobsters and crabs, cover, and cook for 5 minutes. Add the clams and mussels, cover, and cook for another 5 minutes.
In a food processor, combine egg yolks, garlic, lemon juice, basil, cayenne, salt and pepper. Puree until smooth. With the machine running, slowly add the olive oil until the mixture is thick and emulsified.
Thin with a little more lemon juice, if necessary.
*RAW EGG WARNING
Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness. 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.