Melt butter in a large heavy pot over medium heat. Stir in flour and cook, stirring constantly, until the roux reaches a medium brown color (similar to peanut butter), about 5-10 minutes.
Add diced onion, bell pepper, and celery. Stir and cook until softened, about 5 minutes.
Stir in minced garlic and cook for 1 more minute.
Add Cajun seasoning, black pepper, and cayenne. Stir to coat the vegetables.
Slowly whisk in warm seafood or chicken stock, stirring constantly to prevent lumps.
Bring mixture to a simmer and cook for about 10-15 minutes until thickened.
Stir in crawfish tails and cook for 5 minutes, just until heated through. Taste and adjust seasoning with salt if needed.
Serve hot over cooked white rice, topped with chopped parsley and sliced green onions.