In a medium bowl, combine ground beef, bread crumbs, egg, green onions and 1 T.
Cajun seasoning. Form into 4 patties.
In a separate bowl combine the barbeque sauce and the 1 t. Cajun seasoning. Mix
well and set aside.
Grill the patties until the desired doneness, 11 - 13 minutes. Top with the
cheese. Serve with the barbeque sauce. (You can lightly brush it on both sides
of the burger before putting on the cheese.)