Place a large, heavy pot over medium heat, melt butter, and drizzle in olive oil.
Next, add the onion, garlic, celery, carrot, and thyme. Cook until the vegetables are soft and the garlic is fragrant, stirring occasionally for about 5 minutes.
Then add the tomato paste and simmer until it coats the vegetables, about 2 minutes.
Sprinkle flour over the vegetables and cook until smooth and the flour fully absorbs the fat, about a minute. (That helps to thicken the soup later.)
Add the wine, Worcestershire sauce, Creole seasoning, paprika, cayenne, pepper, and bay leaf. Then stir to thoroughly combine all the ingredients.
Next, add the seafood stock. Reduce the heat and let your bisque simmer until the liquid is reduced and the flavors meld, stirring occasionally for 8-10 minutes.
Taste and season it with salt and pepper as needed.
Remove the bay leaf and pour the bisque into a blender. Puree in small batches to prevent pressure from building up inside.
Return the bisque to the pot, placing it over medium to low heat, and stir in the heavy cream and half of the crabmeat.
Simmer until it's just warmed through, about 5 minutes. Divide the bisque among your serving bowls and top with the remaining crabmeat. Garnish with chives before serving, and enjoy!