In a medium mixing bowl combine egg, the 1/4 cup bread crumbs, and green onion.
Add meat; mix well.
Shape meat mixture into eight 1/4 -inch-thick patties, 4 inches in diameter.
For stuffing, in a small bowl combine carrot, chutney, and the 1 tablespoon bread crumbs.
Spoon about 7 rounded tablespoon of the stuffing mixture over half of the patties.
Spread to within 1/2 inch of edges.
Top with remaining patties.
Press meat around edges to seal well.
Arrange patties on the cooking grill.
Grill 11 to 12 minutes or till no pink remains, turning once halfway through grilling time.
Serve on toasted buns.