Step 1: In a large heavy-bottomed pot or Dutch oven, heat the olive oil and butter over medium heat. Add the diced onion, celery, and carrots. Sauté for 8-10 minutes, or until softened and translucent, stirring occasionally.
Step 2: Add the minced garlic and cook for another minute until fragrant. Pour in the dry sherry (or wine) and deglaze the pot, scraping up any browned bits from the bottom. Cook until the liquid has almost evaporated.
Step 3: Stir in the tomato paste, Old Bay seasoning, smoked paprika, and cayenne pepper (if using). Cook for 2-3 minutes, stirring constantly, to toast the spices and deepen the flavor.
Step 4: Pour in the seafood stock. Bring the mixture to a simmer, then reduce heat to low, cover, and let it gently simmer for 15-20 minutes, allowing the flavors to meld.
Step 5: Using an immersion blender, carefully blend the soup until smooth. Alternatively, transfer the soup in batches to a regular blender (be cautious with hot liquids and vent the lid). Strain the soup through a fine-mesh sieve for an extra silky texture, pressing on the solids, then return the strained liquid to the pot.
Step 6: Gently stir in the half-and-half or heavy cream. Add the picked crab meat and chopped shrimp. Cook on low heat for 5-7 minutes, or until the shrimp are pink and cooked through and the bisque is heated through. Do not boil once cream is added.
Step 7: Season the bisque with salt and black pepper to taste. Ladle into bowls, garnish with fresh chopped parsley, and serve immediately with crusty bread.