In a large saucepan or stockpot, bring the whole milk to a gentle simmer over medium heat. Add the kosher salt and stir until completely dissolved. Remove from heat and allow the milk to cool completely before stirring in the buttermilk.
Place the spatchcocked turkey in a large, food-safe brining bag or container. Pour the cooled buttermilk brine over the turkey, ensuring it is evenly coated. Seal the bag, place it in a large roasting pan or pot to catch any leaks, and refrigerate for 24–36 hours, turning occasionally to redistribute the brine.
Remove the turkey from the brine, discard the brine, and pat the turkey thoroughly dry with paper towels. Place the turkey breast-side up on a large roasting tray. In a small bowl, combine the softened butter with the finely chopped thyme, sage, and rosemary. Rub the herb butter generously over the entire turkey, including underneath the skin where possible.
Allow the turkey to rest. Let the prepared turkey sit at room temperature for up to 1 hour before cooking.
Preheat the Traeger or oven. For a subtly smoky flavor, preheat your Traeger grill to 375°F with the lid closed. Alternatively, preheat your oven to 375°F if roasting indoors.
Traeger method: Place the turkey breast-side up directly on the grill grates, with a drip pan underneath if desired. Grill for approximately 2–2½ hours, depending on the size of the turkey and your grill’s temperature.
Oven-roasted method: Place the turkey breast-side up on a wire rack set inside a large roasting pan or rimmed baking sheet. Roast at 375°F for approximately 2–2½ hours, depending on the size of the turkey.
Check for doneness. Begin checking the internal temperature before the estimated cooking time is up. The thickest part of the breast and thigh should reach 165°F, without the thermometer touching the bone. If the skin begins to brown too quickly, loosely tent the breast with aluminum foil.
Carefully transfer the turkey to a large cutting board or serving platter. Allow it to rest for 20–30 minutes before carving to help retain its flavorful juices. Serve warm with homemade turkey gravy and your favorite Thanksgiving sides.