Heat oil in a 6-quart Dutch oven or stockpot set over medium heat.
Add the sliced fennel and shallots; cook for 6 minutes, stirring occasionally.
Stir in garlic, salt, and black pepper; cook for 2 more minutes.
Add tomato paste; stir to combine.
Stir in diced tomatoes, seafood or chicken stock, and wine.
Add bay leaf; cover and bring to a simmer.
Reduce heat to medium-low and continue to simmer covered for 10 minutes.
Remove cover and add the clams and mussels; cover and cook for 4 minutes, or until clams and mussels begin to open.
Add the cod; cover and cook for 3 minutes.
Add in the shrimp and cook uncovered for 2 to 3 more minutes, or until cooked through. Stir occasionally.
Remove from heat. Taste soup for salt and pepper; adjust accordingly.
Discard any clams and mussels that didn’t open.
Remove bay leaf.
Garnish with parsley and red pepper flakes.
Serve with lemons.