Prepare the “brine” by whisking together the buttermilk, salt, hot sauce and granulated garlic. Rinse and dry the turkey breast. Place in a large, zip-top bag and pour in the brine. Remove excess air, seal and refrigerate for 12 to 24 hours.
About 45 minutes before cooking, remove the breast from the brine. Pat dry, and season liberally with Triple S Rub on all sides. Let the turkey rest and rise toward room temperature.
Prepare the grill for roasting (indirect grilling) at 350°F with wood smoke from foil smoking envelopes.
Place the breast directly on the grill grate in the indirect zone with the skin side up. Place the smoking envelope above the fire. Close the hood and roast at 350°F for about 1 hour. After the first 30 minutes, brush the top of the breast with olive oil. After the full hour, raise the temperature to 400°F to crisp up the skin (either turn the heat up on the grill, add some dry wood chips to the hottest zone of the grill, or move the breast to a warming rack elevated above the hottest part of the grill) and finish roasting the turkey until the internal temperature reaches 155°F. Remove from the grill and let rest for 5 minutes while the internal temperature rises to 165°F.
Slice the breast away from the bones, and then slice crosswise into 1/2 inch thick pieces.
Tips for Preparing this Recipe on a Kalamazoo Hybrid Grill
A Kalamazoo K750 Series Hybrid Fire Grill will hold the desired 350° temperature with a single main burner running on medium. Preheat the grill with all main burners on high, then turn off two adjacent main burners and the ignition burner. Turn the remaining main burner to medium to cook the turkey.
Place the smoking envelope inside the Hybrid Fire Grilling Drawer above the active burner. When it comes time to bump the temperature, toss a handful of wood chips directly into the drawer above the burner. Place the turkey breast with the skin side down on the warming rack above these wood chips to finish cooking.