Mix the turkey, Cajun seasoning, apple, 1/4 cup green onions and the panko in a bowl; season with salt and pepper.
Form into four 1-inch-thick patties. Refrigerate.
Whisk the mayonnaise and chutney in a large bowl.
Add the cabbage, carrot and the remaining 1/4 cup green onions, season with salt and pepper and toss to coat.
Brush a cast iron pan (or a regular nonstick pan) with canola oil.
Cook the turkey patties until browned and cooked through, 6-7 minutes per side.
Check for doneness with a meat thermometer - burgers are ready when they reach 165 degrees F.
Brush the cut sides of the buns with mayonnaise and sprinkle with Cajun seasoning; put on broiler pan and broil in oven for about 2 minutes until slightly browned.
Serve the burgers and slaw on the buns.