Preheat grill to medium-high heat. Brush grill with canola oil.
Cut the bananas in half, lengthwise and grill, skin side down just until warm. Remove warmed banana from the skin and cut again in half.
On a piece of aluminum foil, place 1 cookie. Top evenly with banana slices, marshmallows, chocolate chips, graham cracker crumbs and top with another cookie. Wrap foil around the sandwich and place on the grill until warmed through and melted.