Whisk together apple cider vinegar, honey and 2 tablespoons vegetable oil in a large bowl. Fold in sliced cabbage, grated apple, dried cranberries and parsley leaves. Toss to coat. Salt and pepper to taste. Refrigerate until ready to serve.
Preheat the oven to 400 degrees F. Wash the sweet potato and prick with a fork in several places. Place directly on the oven rack. Bake until very soft, about 45 minutes.
Remove the sweet potato from the oven, allow to cool, then peel and mash with a fork.
Mix the mashed sweet potato with the ground turkey, bread crumbs, egg, onion powder, minced garlic, rosemary, minced thyme and salt and pepper in a large bowl. Mix well and form into 4 patties. Heat a large skillet over medium heat. Add 1 tablespoon vegetable oil, then cook the turkey patties for 5-6 minutes per side, adding the cheese on the second side.
To assemble, spread the cranberry mayo on the bottom side of each bun, add a turkey patty and top with slaw.
In a small bowl, whisk together cranberry sauce, mayonnaise, dijon mustard, lemon juice and salt until well combined.