Step 1: Make the Shrimp Stock

1. Place the reserved shrimp shells in a medium saucepan with 4 cups of water or seafood stock.
2. Add a bay leaf and simmer for 15–20 minutes to extract the shrimp flavor. Strain and set aside, discarding the shells. This stock will serve as the flavorful base for your bisque.

Step 2: Sauté the Vegetables

1. In a large pot or Dutch oven, heat the butter and olive oil over medium heat.
2. Add the chopped onion, celery, and carrot. Sauté for 5–7 minutes, stirring occasionally, until the vegetables are softened but not browned.
3. Stir in the minced garlic and cook for an additional 1–2 minutes, being careful not to burn it.

Step 3: Build the Bisque Base

1. Sprinkle the flour over the sautéed vegetables, stirring constantly to create a roux. Cook for 2–3 minutes, or until the flour loses its raw smell.
2. Slowly whisk in the shrimp stock, ensuring there are no lumps. Add the white wine, stirring well to combine.
3. Bring the mixture to a gentle simmer, then add the smoked paprika, cayenne pepper, dried thyme, salt, and black pepper. Stir well to distribute the spices.

Step 4: Add the Corn and Cream

1. Stir in the corn kernels and simmer the bisque for 10–15 minutes, allowing the flavors to meld.
2. Reduce the heat to low, then slowly add the heavy cream and milk, stirring constantly. Allow the bisque to heat through but do not let it boil, as this could cause the cream to curdle.

Step 5: Cook the Shrimp

1. Add the peeled and deveined shrimp to the bisque. Simmer for 3–5 minutes, or until the shrimp turn pink and are cooked through. Be careful not to overcook the shrimp, as they can become rubbery.

Step 6: Blend (Optional)

For a smoother bisque, use an immersion blender to blend part of the soup, leaving some chunks for texture. Alternatively, transfer half of the soup to a blender, blend until smooth, and return it to the pot.

Step 7: Adjust Seasonings and Serve

Taste the bisque and adjust the seasoning with additional salt, pepper, or cayenne if needed. Remove the bay leaf before serving. Ladle the bisque into bowls and garnish with fresh parsley or chives and a sprinkle of paprika. Serve with crusty bread or oyster crackers on the side.