Preheat the oven to 375ºF.
Place the garlic on a square of aluminum foil. Sprinkle with the salt and drizzle with 1/2 teaspoon of the olive oil. Gather the corners of the foil together to make a pouch and seal. Roast for 30 minutes, or until the garlic is soft when tested with a fork. Holding each clove between your thumb and index finger, pop out the garlic from the skin.
Place the garlic and egg in a food processor and blend for 10 seconds. Add the lemon juice. With the motor running, slowly add the remaining 1/2 cup olive oil through the feed tube. The mixture will be thick, like mayonnaise. Add the parsley, salt, and cayenne and pulse 3 to 4 times to blend. Can be stored up to 24 hours in a covered container in the refrigerator.
Season the fish with 2 teaspoons of the salt and 1/4 teaspoon of the cayenne. Combine the onions, bell peppers, celery, and garlic in a bowl and season with the remaining 2 teaspoons salt and remaining 1/2 teaspoon cayenne.
Melt the butter in a large cast-iron or enameled cast-iron Dutch oven over medium heat. Place one third of the mixed vegetables on top of the butter, stirring to coat with the butter. Spread the vegetables evenly on the bottom of the pot. Place one third of the tomatoes and 2 of the bay leaves on the vegetables. Place one third of the fish on top of the vegetable and tomato mixture. Layer the vegetables, tomatoes, bay leaves, and fish 2 more times. Scatter the shrimp on top. Add the wine down the side of the pot. Cover and reduce the heat to medium-low. Cook for 1 hour without removing the lid. Remove the bay leaves.
Serve in large soup bowls and garnish with parsley. Drizzle 1 tablespoon of the rouille in each bowl. Serve immediately.
Yield: 8 to 10 servings