Preheat broiler. Line broiler pan with aluminum foil. Spray foil with vegetable cooking spray.
In a small bowl, combine mayonnaise, mustard, parsley, lemon juice and tabasco sauce. Mix well. One a sheet of waxed paper, combine bread crumbs and tarragon. Mix well. Dip shrimp in mayonnaise mixture, turning to coat. Dredge shimp in bread crumb mixture, turning to coat and patting so crumbs adhere. Place shrimp on prepared pan. Broil 4 inches from heat, turning once, until golden brown, about 5 minutes.