1. Sauté the Vegetables: In a large pot, heat the butter and olive oil over medium heat. Add the chopped onion, bell pepper, and minced garlic. Cook until the vegetables are softened, about 5-7 minutes.

2. Create the Roux: Stir in the all-purpose flour and cook for 1-2 minutes, stirring constantly, to form a roux. This will help thicken the bisque.

3. Add the Liquids: Gradually whisk in the seafood or chicken broth, followed by the heavy cream. Bring the mixture to a gentle simmer.

4. Incorporate the Corn and Spices: Stir in the corn kernels, smoked paprika, cayenne pepper, dried thyme, salt, black pepper, Worcestershire sauce, and hot sauce (if using). Allow the bisque to simmer for 5-7 minutes, letting the flavors meld together.

5. Cook the Shrimp: Add the peeled and deveined shrimp to the simmering bisque and cook until the shrimp are pink and opaque, about 3-4 minutes.

6. Serve and Enjoy: Ladle the New Orleans Shrimp and Corn Bisque into bowls, garnishing each serving with sliced green onions and chopped fresh parsley.