Prep the shrimp: Peel and devein the shrimp. Save the shells in a bowl.
Roughly chop half the shrimp and leave the rest whole. Keep shrimp chilled.
Build a quick shell stock: In a medium pot, add the shells and 4 cups water (or seafood stock). Bring to a simmer and cook 15–20 minutes.
Strain and discard shells. Keep the hot stock nearby.
Sweat aromatics: In a large pot, heat butter and olive oil over medium heat. Add onion and celery with a pinch of salt.
Cook 5–7 minutes until soft and translucent, not browned. Stir in garlic for 30 seconds.
Add cauliflower and spices: Stir in cauliflower, tomato paste, smoked paprika, and cayenne (if using). Cook 2 minutes to toast the spices and caramelize the paste slightly.
Deglaze: Pour in sherry or white wine.
Scrape up any browned bits. Let it bubble for 1–2 minutes to reduce the alcohol.
Simmer: Add the hot shell stock and bay leaf. Bring to a gentle simmer and cook 12–15 minutes, until the cauliflower is very tender.
Blend smooth: Remove the bay leaf.
Use an immersion blender to puree the soup until velvety. Or transfer carefully to a blender in batches and blend until smooth. Return to the pot.
Finish the base: Stir in 3/4 cup heavy cream.
Taste and season with salt and black pepper. Add more cream if you prefer a richer texture.
Cook the shrimp: Bring the bisque to a gentle simmer (not a rolling boil). Add the chopped shrimp first and cook 1–2 minutes.
Add the whole shrimp and cook another 2–3 minutes until just opaque and pink.
Brighten and serve: Squeeze in 1–2 teaspoons lemon juice to lift the flavors. Ladle into bowls and top with chopped parsley or chives. Add a pinch of smoked paprika on top if you like.