Heat olive oil in a large pot over medium heat. Add the diced onion and cook until translucent, about 3-5 minutes.
Stir in the minced garlic and cook for an additional minute until fragrant.
Pour in the white wine (if using) to deglaze the pot, scraping any brown bits from the bottom. Allow the wine to reduce by half, which should take about 2 minutes.
Add the tomato paste, paprika, and cayenne pepper. Cook for another minute, stirring constantly.
Pour in the broth and add the bay leaf. Bring the mixture to a simmer.
Once simmering, add the shrimp and cook until they turn pink and are cooked through, about 5-7 minutes.
Remove the shrimp with a slotted spoon, leaving the broth mixture in the pot. Set aside a few shrimp for garnish, if desired.
Using an immersion blender, puree the broth mixture until smooth. Alternatively, carefully transfer the mixture to a blender and puree in batches.
Return the pureed mixture to the pot (if using a blender) and add the heavy cream. Stir well to combine.
Chop the cooked shrimp into bite-sized pieces and add them back into the pot. Warm the bisque over low heat, making sure it does not boil.
Stir in the butter until melted and fully incorporated. Season with salt and black pepper to taste.
Serve hot, garnished with fresh parsley and reserved whole shrimp.