Melt butter in a large saucepan over medium heat. Whisk in flour and cook, stirring constantly, until golden brown, about 5 minutes. Add onion, celery, bell pepper, garlic, thyme, paprika, salt and cayenne pepper; cook and stir until vegetables are softened and lightly browned, about 5 minutes.
Add chicken broth or seafood stock; bring to a boil. Reduce heat to low; simmer for 10 minutes.
Stir in crawfish tails; cook just until heated through.