Heat the olive oil in a large pot over medium heat. Add the onion, celery, and bell pepper, and sauté until they are soft and translucent, about 5-7 minutes.
Stir in the garlic and cook for an additional 1-2 minutes until fragrant.
Sprinkle in the flour and cook, stirring constantly, for 2 minutes to remove the raw flour taste.
Gradually whisk in the seafood stock, ensuring there are no lumps, and bring the mixture to a simmer. Cook for 10-15 minutes, stirring occasionally, until it slightly thickens.
Add the crawfish tails, heavy cream, cajun seasoning, and black pepper to the pot. Simmer for another 15-20 minutes until the flavors meld together.
Taste and adjust seasoning if necessary. Serve hot, garnished with sliced scallions and chopped parsley.
Notes
For a spicier version, add a pinch of cayenne pepper.