Step 1

Cut 1 onion half into 4 wedges, leaving root end attached. Cut 1 celery stalk in half crosswise; set remaining onion and celery aside. Combine onion wedges, celery halves, 5 cups water, bay leaf, black pepper, and 1/4 teaspoon salt in a large saucepan. Bring to a boil over medium-high. Fill a medium bowl with ice water; set aside.

Step 2

Add shrimp to boiling water mixture in saucepan; cook until opaque and cooked through, 2 to 3 minutes. Using a slotted spoon, transfer shrimp to prepared ice bath. Add mussels to saucepan; cook until mussels open, 2 to 3 minutes. Transfer mussels to ice bath, discarding any mussels that did not open. Add scallops and squid to saucepan; cook until scallops and squid rings turn opaque, about 1 minute. Using a slotted spoon, transfer scallops and squid to ice bath. Reserve water mixture in saucepan.

Step 3

Remove shrimp and mussels from ice water, and drain in a colander. Peel shrimp, and shuck mussels, reserving some mussels in shells for garnish, if desired; reserve shrimp and mussel shells. Add reserved shells and reserved scallop side muscles to water mixture in saucepan; bring to a boil over medium-high. Reduce heat to medium-low; simmer, stirring occasionally, until liquid reduces to about 3 cups, 20 to 25 minutes. Meanwhile, remove remaining seafood from ice bath; pat dry, and set aside.

Step 4

Remove saucepan with seafood mixture from heat; pour mixture through a fine wire-mesh strainer into a large heatproof bowl, and discard solids. Set strained stock aside. Wipe saucepan clean.

Step 5

Roughly chop remaining onion half and remaining 2 celery stalks, keeping separate. Add oil to cleaned saucepan; heat over medium. Add onion; cook, stirring often, until softened, 2 to 3 minutes. Stir in celery and carrots; cook, stirring often, until slightly softened but not browning, 4 to 6 minutes. Add tomato paste, parsley, thyme, paprika, crushed red pepper, garlic, and remaining 1 teaspoon salt. Cook, stirring constantly, until mixture is fragrant and vegetables are well coated in tomato mixture,1 to 2 minutes. Stir in reserved seafood stock; cook over medium, stirring occasionally, until flavors meld and mixture reduces to about 3 cups, 10 to 15 minutes.

Step 6

Set aside 4 cooked shrimp and 1/4 cup mixed mussels, scallops, and squid for garnish. Add heavy cream and remaining cooked seafood to stock mixture in saucepan. Reduce heat to low; cook, stirring occasionally, until seafood is heated through, 8 to 10 minutes.

Step 7

Transfer seafood mixture to a blender. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening. Process until smooth, about 1 minute, adding water, 2 tablespoons at a time, if needed to thin bisque to desired consistency. Season with salt to taste.

Step 8

Divide bisque evenly among bowls; garnish evenly with reserved seafood and additional parsley. Serve with baguette.