If using fresh shrimp with shells, peel the shrimp and reserve the shells. Pat both shrimp and crab meat thoroughly dry with paper towels. Finely chop the onion, carrots, and celery. Mince the garlic.

In a large Dutch oven or heavy-bottomed pot, melt the butter with the olive oil over medium heat. Add the chopped onion, carrots, and celery. Sauté for 8-10 minutes, stirring occasionally, until the vegetables have softened and become translucent.

Add the minced garlic and tomato paste to the pot. Cook for another 2 minutes, stirring constantly, until the tomato paste darkens slightly and becomes fragrant.

Sprinkle the all-purpose flour over the sautéed vegetables. Cook for 2 minutes, stirring constantly, to create a roux. This will thicken the bisque.

Pour in the brandy or dry sherry, scraping up any browned bits from the bottom of the pot with a wooden spoon. Cook until the liquid has almost completely evaporated, about 1-2 minutes.

Gradually whisk in the fish stock, a little at a time, until completely smooth and no lumps remain. Bring the mixture to a gentle simmer, then reduce the heat to low, cover the pot, and cook for 30 minutes, stirring occasionally, to allow the flavors to deepen and meld.

Carefully transfer the hot soup mixture to a blender (working in batches if necessary) and blend until completely smooth and creamy. Alternatively, use an immersion blender directly in the pot.

Pass the blended bisque through a fine-mesh sieve back into the clean Dutch oven. Use the back of a spoon to press on any solids in the sieve to extract as much liquid as possible. Discard the remaining solids.

Return the strained bisque to medium-low heat. Stir in the heavy cream, whole milk, Old Bay seasoning, smoked paprika, cayenne pepper (if using), and chopped fresh thyme. Bring the bisque to a gentle simmer, stirring frequently, but do not allow it to come to a rolling boil.

Add the prepared shrimp to the simmering bisque. Cook for 3-5 minutes, or until the shrimp turn pink and opaque. Be careful not to overcook.

Gently fold in the lump crab meat, being careful not to break it up too much. Heat through for just 1-2 minutes until the crab is warmed through.

Stir in the fresh lemon juice. Taste the bisque and adjust seasoning with salt and black pepper as needed.

Ladle the luxurious crab and shrimp seafood bisque into warm bowls. Garnish with fresh chopped parsley and a sprinkle of extra fresh thyme. Serve immediately with crusty bread for dipping.