Bring 1 quart of the water to a simmer (reserve the remaining 2 quarts and cider). Add all of the ingredients for the brine and stir well until the salt and sugar have dissolved.

To a large bowl or pot add the brine and the remaining 2 quarts of water and 1 quart of apple cider. Put in the refrigerator until chilled.

After the brine has cooled, add the turkey breast. Place a plate or bowl on top of the turkey in order to keep the breast submerged.

Brine the turkey in your refrigerator for 6 to 12 hours.

Remove the turkey from the brine, rinse with cool water and completely dry off with paper towels. Place on plate and put it in your refrigerator for 4 to 24 hours to dry. This will help the smoke adhere to the meat.

Heat your smoker to 265 degrees.

Season the breast with the seasoning of your choice. I use kosher salt and fresh cracked pepper.

Insert an instant read thermometer into the meat in the thickest part. Place the turkey in your smoker. The closer to your vent pipe the better. The smoke exiting the smoker will pass by the turkey ensuring a stronger smoke flavor.

Smoke the turkey for 1 hour. Brush the mayonnaise all over the breast. Smoke for 30 more minutes.

Line a oven-safe cooking vessel with 2 layers of heavy duty aluminum foil. Place the turkey in the dish. Place the butter on top of the turkey. Enclose the turkey in the foil by crimping the foil together on top of the turkey breast.

Place back in your smoker and cook until an internal temperature of 160 degrees F is reached. Remove from the smoker and allow to rest and carryover cook at room temperature for 20 to 30 minutes.

Slice across the grain and serve.