Heat gas or charcoal grill. In large bowl, mix ground beef, celery, onion, bell pepper and Cajun seasoning. Shape mixture into 4 flat oval-shaped patties, 1/2 inch thick.
When grill is heated, place patties on gas grill over medium heat or on charcoal grill over medium coals; cover grill. Cook 11 to 13 minutes, turning once, until patties are no longer pink in center and juice is clear and thermometer inserted in center of patties reads 160°F.
To serve, top 4 slices of bread with endive and patties. Spoon 1 tablespoon barbecue sauce on each patty. Cover with remaining bread slices.