Step 1

In a large pot, heat the olive oil. Add the celery, carrots, garlic, chopped fennel and onion, season with salt and cook over moderately high heat, stirring occasionally, until very tender, 20 minutes. Add the thyme and fennel seeds and cook, stirring, until fragrant, 2 minutes. Add the tomatoes and their juices and cook over moderately high heat, breaking them up with a wooden spoon and stirring occasionally, until the tomato liquid is reduced, about 10 minutes. Stir in the stock, beer, fish head and bones, Old Bay and 8 cups of water. Bring to a boil, then reduce the heat to moderate and simmer for 30 minutes.

Step 2

Strain the fish stock through a fine sieve set over a very large pot, pressing on the solids; discard the solids. Season generously with salt. Bring the stock to a boil over high heat, add the potatoes and cook until barely tender, 15 to 17 minutes. Add the clams and chorizo, cover and cook for 2 minutes. Add the corn, cover and cook for 4 minutes. Season the fish fillets with salt and pepper and add to the stew. Cover and cook for 2 minutes. Add the crabs, cover and cook for 3 minutes. Finally, add the shrimp, cover and cook until all of the seafood is cooked through and the potatoes and corn are tender, about 5 minutes more. Using a slotted spoon, transfer the seafood, potatoes and corn to 2 large platters. Alternatively, spread the seafood on a paper-lined table. Garnish with celery leaves, cilantro leaves and parsley leaves and serve immediately with the Old Bay aioli, lemon wedges, hot sauce and melted butter. Reserve the fish stock for another use.