Whisk the Greek yogurt with the cider vinegar, green apple, carrot, red cabbage, and raisins. Season with salt and pepper. Cover and chill for 2 hours.
In a large bowl, combine the egg white, bread crumbs, applesauce, onion, sage, pepper, nutmeg, brats, and ground turkey. Mix with your hands to combine. Shape into 2 large patties.
Preheat your grill to medium heat and clean grate.
Grill the patties, 14 to 18 minutes until internal temperature reaches 165 degrees F, flipping once, halfway through cook time.