In a large pot, melt 1 tablespoon of butter over medium heat. Add shrimp shells and cook for 5 minutes until pink. Add seafood stock, bring to a simmer, and cook for 15 minutes. Strain and reserve stock; discard shells.
In the cleaned pot, melt remaining 3 tablespoons of butter over medium heat. Add onion, celery, and carrot. Sauté for 8 minutes until translucent.
Stir in garlic and tomato paste, cooking for 2 minutes until the paste is fragrant and darkens slightly.
Whisk in the flour and cook for 2 minutes to create a roux, ensuring it does not burn.
Deglaze the pot with dry sherry, scraping the bottom to release any browned bits.
Gradually whisk in the reserved seafood stock until smooth. Add thyme, bay leaf, paprika, and cayenne pepper.
Simmer uncovered for 20 minutes. Remove the bay leaf.
Using an immersion blender, puree the soup base until completely smooth. For an extra-fine texture, pass the liquid through a fine-mesh sieve.
Lower the heat and stir in the heavy cream. Bring to a gentle simmer.
Add the raw shrimp to the pot and cook for 3 to 5 minutes until pink and opaque. Gently fold in the crab meat and heat through for 2 minutes.
Stir in lemon juice and season with salt and pepper to taste. Garnish with fresh chives before serving.