Heat a large pot over high heat. Add 1 tablespoon olive oil and heat. Add the chorizo and cook until some of the fat is rendered and the chorizo starts to brown. Add the onions, garlic, fennel, and red pepper flakes and cook until the onions begin to brown, about 6 to 7 minutes. Add the bay leaves and thyme, and season with salt and pepper.
Deglaze with the white wine.
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.
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. Add the parsley and season with salt and pepper, to taste.
Spread the aioli on toasted French bread slices and serve with the soup.
2 egg yolks*
1 clove garlic
1/2 lemon, juiced
1/2 cup basil leaves
Salt and freshly ground pepper
1 1/2 cups olive oil
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.