Cook the Aromatics: Heat the olive oil and butter in a large Dutch oven over medium-high heat until the butter is melted and begins to foam. Add the chopped fennel and onion, sautéing for approximately five minutes or until softened and fragrant. Stir frequently to prevent browning. Incorporate the garlic, thyme, paprika, saffron, and cayenne pepper, and cook briefly—about 20 seconds—until aromatic.
Deglaze with Wine and Add Liquids: Pour in the dry white wine, stirring and scraping up any browned bits from the bottom of the pot. Allow the wine to simmer for one minute to reduce slightly. Add the clam juice (or seafood stock), canned diced tomatoes with their juices, and the bay leaves. Stir gently to combine all ingredients.
Simmer the Base: Bring the mixture to a gentle boil, then reduce the heat to medium. Let it simmer for 8 to 10 minutes, or until the liquid has reduced by approximately half, intensifying the flavors and thickening slightly.
Prepare and Add the Fish: Lightly season the halibut pieces with salt and freshly ground black pepper. Gently place them into the simmering broth. Lower the heat to medium-low, cover the pot, and cook for two minutes to allow the fish to begin absorbing the flavors.
Incorporate the Shellfish: Carefully add the mussels and scallops to the pot. Cover once more and cook for three minutes, allowing the mussels to begin opening. Then, remove the lid, add the shrimp, and cover again. Continue cooking for an additional two to three minutes, or until the shrimp are opaque, the mussels have fully opened, and the scallops are firm yet tender.
Finish and Adjust Seasoning: Remove the bouillabaisse from the heat. Discard the bay leaves and any unopened mussels. Stir in the freshly chopped basil and parsley, then taste the broth and adjust seasoning with additional salt or pepper if necessary.
Serve and Garnish: Ladle the bouillabaisse into wide, shallow bowls. Garnish with a sprinkle of red pepper flakes if desired. Serve immediately with toasted baguette slices for dipping, allowing each guest to enjoy the vibrant, saffron-scented broth.