In a large skillet over medium heat, melt the butter.
Add flour to the skillet, stirring continuously to create a roux. Cook until the roux turns a light brown color, about 5 minutes.
Add the onion, green bell pepper, celery, and garlic to the skillet. Cook until vegetables are soft, about 5 minutes.
Gradually stir in chicken broth and water, followed by Cajun seasoning, paprika, thyme, and cayenne pepper. Bring to a simmer.
Add the crawfish tails to the skillet and simmer for about 10 minutes, or until the sauce thickens.
Season with salt and black pepper to taste. Stir in the green onions and parsley.
Serve the etouffee over cooked rice.