In a large stockpot, (not the 24-quart extra large one), add the oil over medium heat. When the oil is hot and silky, add the carrots, celery, garlic and onion and season with salt and pepper. Cook, stirring occasionally until tender, about 20-25 minutes.
Add thyme and fennel seeds and cook to release their flavor, about 2 minutes.
Add the tomatoes along with their juices and break them up, I use a square-head potato masher to break them up more efficiently. Cook, stirring occasionally to let all the flavors come together, about 10 minutes.
Add the chicken stock, beer, fish head and bones, Old Bay seasoning, and 8 cups of water. Allow everything to come to a full boil. Reduce heat to low and let the pot simmer for about 30-40 minutes.
Grab the 24-quart stockpot and add 1 tablespoon of olive oil. Add the sausage, browning the pieces on both sides, cook until almost done, 10 minutes or so.
Add the potatoes. Cook only until they are slightly tender, about 15 minutes.
Add the clams. Cover and cook 2 minutes.
Add the corn, cover and cook, 4 minutes.
Season the snapper fillets with salt and pepper on both sides and add to the pot. Cover and cook 2 minutes.
Add the crabs, cover and cook 3 minutes.
Finally add the mussels, cover and cook. Cook until all the seafood is properly cooked through, about 5 minutes more. Being sure to discard any clams and mussels that didn’t open.
Using a slotted spoon transfer the seafood, corn, potatoes and sausage to platters for serving or if planning to display on the table bring the hot pot to a paper-lined table and using a slotted spoon transfer the contents to the center of the table, or tip the pot on its side to wow your guests with what comes tumbling out. Spread the contents out nicely along the center of the table.
Garnish with parsley and serve with lemon wedges, melted butter and garlic, and mayonnaise flavored with a squeeze of lemon and Old Bay seasoning. Reserve the stock for another use.