• 3/4 pound cleaned squid
• 2 tablespoons extra-virgin olive oil plus more for drizzling
• 1 celery stalk, finely chopped
• 1 medium carrot, finely chopped
• 1 small onion, finely chopped
• 4 small garlic cloves, gently smashed and peeled
• 1 (3-inch) serrano chile, finely chopped
• 3/4 cup finely chopped flat-leaf parsley
• 3/4 cup dry white wine
• 1 (2 1/2 to 2 3/4-pound) whole red snapper, fillets removed and cut crosswise into 2-inch pieces, head removed and reserved, bones cut into pieces
• 1 (1- to 1 1/2-pound) whole black sea bass, fillets removed and cut crosswise into 2-inch pieces, head removed and reserved, bones cut into pieces
• 4 whole red mullet (about 1 1/4 pounds), cleaned
• 1 (28-ounce) can whole tomatoes in juice (preferably San Marzano)
• 1/2 pound monkfish fillet, cut crosswise into 1-inch pieces
• Medium coarse sea salt
• 12 large whole shrimp in shell, preferably with heads
• 6 large slices peasant bread, toasted

Rinse squid under cold water, then pat dry between paper towels. Halve large tentacles lengthwise and cut bodies (including flaps, if attached) crosswise into 1-inch-wide rings.

In a large, heavy-bottomed pot or Dutch oven, heat oil over medium-high heat. Add celery, carrot and onion; reduce heat to medium and cook, stirring occasionally, until softened, about 7 minutes. Add garlic and chile; cook for 2 minutes more. Add parsley and cook for 2 minutes more.

Add squid, 1 1/2 cups water and wine. Bring to a gentle simmer, reduce heat to low and cook for 20 minutes. Using a slotted spoon, transfer squid to a bowl. Add fish heads and bones, mullet, and tomatoes and juices to pot; bring to a gentle simmer and cook for 30 minutes.

Transfer the heads of the snapper and bass to a large plate. Using your fingers, remove and put into the pot all of the meat and pulp from the cheeks and larger bones; discard heads. Remove large bones from pot and discard. Using the disk with the largest holes, pass remaining contents of pot, including the mullet heads, through a food mill into a large bowl (use a spatula to scrape the puréed fish from the bottom of the disk into the bowl and discard any remaining bones as you go).

Put contents of bowl back into pot. Add squid, monkfish and 1/2 teaspoon salt. Bring to a gentle simmer and cook for 10 minutes. Add snapper and bass fillet. Return to a simmer and cook 10 minutes more. Add shrimp, return to a simmer and cook until shrimp are opaque, about 5 minutes more. Season with salt.

Divide toast among 6 large soup bowls. Ladle soup over top, drizzle with oil, sprinkle with salt and serve.