Melt butter in a large skillet. Add onion, celery, and garlic. Cover and cook 5 minutes or until tender. Stir in parsley, salt, pepper, and crayfish meat. Add breadcrumbs, mixing well. Stuff mixture into empty heads.
Roll heads in flour. Place in a single layer in fryer basket. Fry in deep hot oil (350°) for 3 minutes or until lightly brown; drain. Keep warm until ready to serve.