Preheat a grill or grill pan to medium high. Mix the turkey, jerk seasoning, apple, 1/4 cup scallions and the panko in a bowl; season with salt and pepper. Form into four 1-inch-thick patties and make a small indentation in the middle of each with your thumb to prevent it from puffing up on the grill. Refrigerate.
Whisk the mayonnaise and chutney in a large bowl. Add the cabbage, carrot and the remaining 1/4 cup scallions, season with salt and pepper and toss to coat.
Brush the grill with canola oil. Grill the turkey patties until browned and cooked through, 4 to 5 minutes per side.
Brush the cut sides of the buns with mayonnaise and sprinkle with jerk seasoning; toast on the grill, about 30 seconds. Serve the burgers and slaw on the buns.
Per serving: Calories 504; Fat 20 g (Saturated 3 g); Cholesterol 51 mg; Sodium 894 mg; Carbohydrate 51 g; Fiber 4 g; Protein 36 g