Prepare the dry brine. Add all dry brine ingredients to a small bowl and mix together well.
Brine the turkey. Place the turkey on a wire cooling rack on top of a sheet tray. Pat dry with paper towels. Sprinkle the dry brine liberally all over the entire turkey. Place the sheet tray with the turkey in the refrigerator uncovered to brine overnight, preferably for 24 hours. *TIP – Make sure that you clear enough space in your refrigerator to accommodate the size of the sheet tray and the height of the turkey.
Preheat pellet grill or smoker. After the 24 hour brining period, remove the turkey from the refrigerator. Preheat grill to 325°F with your choice of wood or pellets. Set up the rotisserie motor/attachment on the grill.
Truss the turkey on the rotisserie rod. Slide the rotisserie rod through the turkey cavity and press the forks into the turkey (one fork on either end). Tighten the screws of the forks, or prepare the rotisserie according to manufacturer's instructions. Use butcher’s twine to tie the legs up and around the prongs, holding the turkey in place on the rotisserie rod. Then, tie up the wings so that they are snug against the side of the turkey.
Attach the rotisserie spit to the grill. Attach the rotisserie rod to the motor/attachment according to instructions. Start the rotation and close the lid to begin cooking.
Make the basting butter. Finely chop the fresh thyme and sage. In a small saucepan, heat one stick butter with the thyme and sage until melted.
Baste and cook the rotisserie turkey. About 1½ hour into the cooking time, begin basting the turkey. Use a sprig of rosemary as a brush, dip into the melted butter, and brush on the turkey as it rotates. Close the lid and continue to cook. Baste the turkey with the herb butter every 30-40 minutes until it's done cooking. *TIP – Be sure to save enough of the herbed butter for one last basting when the turkey comes off the smoker.
Cook rotisserie turkey until done. Cook the rotisserie turkey on the grill until the internal temperature of the thickest part of the breasts reaches about 162°F. This allows for carryover cooking during the resting period.
Rest and serve. When the turkey reaches the correct internal temp, carefully remove the rotisserie rod from the grill using heat-proof gloves. Transfer turkey to a cutting board, cut off the twine, and allow the turkey to rest for at least 30 minutes. Then carve and serve.