Prepare rice according to package directions.
Melt 4 tablespoons butter in a large Dutch oven over medium-high heat; add crawfish, and cook 5 minutes or until thoroughly heated. Remove crawfish, and keep warm.
Add onion, bell pepper, and celery to Dutch oven. Cook over medium-high heat 8 minutes or until tender. Add garlic, and cook 1 minute. Remove vegetables, and keep warm.
Melt remaining 6 tablespoons butter in Dutch oven over medium heat. Add flour, and cook, stirring constantly, 20 minutes or until caramel colored. Reduce heat to low, and gradually stir in chicken broth and next 5 ingredients. Cook over medium heat 10 minutes or until slightly thickened. Stir in vegetables and crawfish; cook 5 minutes. Serve with rice.
Note: To freeze, divide étouffée evenly into 3 (1-quart) zip-top plastic freezer bags. Freeze up to 1 month. Thaw in refrigerator overnight. Remove from freezer bag, and warm in saucepan, stirring until thoroughly heated. Each bag contains about two servings.