Remove backbone from turkey using a pair of kitchen shears.
Place turkey on a wire cooling rack on a baking sheet. Dry off the turkey with paper towels to get as much moisture off the skin as possible. Season with salt, pepper, and garlic, and return to the refrigerator overnight.
Place turkey on countertop and light grill, setting up for indirect heat. Preheat grill temperature to 225°F.
Once the grill is preheated, place a reliable leave-in thermometer in the thickest portion of the breast and place turkey on the grill. Close the lid and allow the turkey to cook until the internal temperature reaches 110°F in the breast.
While turkey is cooking, add 2 cups cider vinegar to a medium saucepan over medium-high heat. Once vinegar starts to boil, reduce heat to low and whisk in remaining ingredients for the glaze. Continue to whisk until brown sugar and salt have dissolved. Divide glaze in half and set aside.
When the turkey reaches 110°F internal temperature, increase grill temperature to 350°F. Using a high-temp silicone glazing brush, coat the entire surface of the turkey with glaze. Reapply the glaze every 15 minutes till the turkey reaches 150°F internal temperature in the breast.
Remove turkey, tent with foil, and let rest until the internal temperature of the turkey has reached ~165°F as read on your leave-in thermometer.
Slice and serve with the remaining half of the glaze to be used as a dipping sauce for the turkey.