Making the New Orleans Shrimp and Corn Bisque is simple if you follow these steps:

1. Prepare the Ingredients: Gather and chop all your ingredients before beginning the cooking process.
2. Sauté the Vegetables: In a large pot, heat the olive oil and butter over medium heat. Add the chopped onions and bell peppers, cooking until softened (about 5-7 minutes).
3. Add Garlic and Spices: Stir in the minced garlic, thyme, paprika, and cayenne pepper (if using), cooking for an additional 2 minutes until fragrant.
4. Add the Stock: Pour in the fish stock or chicken broth, bringing the mixture to a simmer. Allow it to cook for 10 minutes to let the flavors meld.
5. Incorporate the Corn: Add the sweet corn and simmer for another 5 minutes.
6. Add the Shrimp: Carefully mix in the shrimp, cooking until they turn pink and opaque (about 3-5 minutes).
7. Blend the Mixture: For a smooth bisque, use an immersion blender to carefully blend the soup until it reaches a creamy texture. (Alternatively, transfer to a blender in batches.)
8. Finish with Cream: Stir in the heavy cream, mixing well. Allow it to heat through but not boil. Season with salt and pepper to taste.
9. Garnish and Serve: Remove from heat and ladle into bowls. Garnish with fresh parsley before serving.

These detailed steps will guide you in creating an incredible New Orleans Shrimp and Corn Bisque that impressively combines flavors and comfort.