Place mayonnaise, vinegar, honey, onion powder and salt in a medium sized bowl and whisk to combine. Add the cole slaw and red cabbage to the bowl and toss to coat, set aside.
Combine ground turkey, carrot, soy sauce, ginger, garlic, parsley, salt and pepper, mixing with your hands until well blended. Form patties. Heat the grill to 400-500 degrees. Place burgers on the grill and close the lid. Cook for 18-20 minutes turning once.