Place turkey breast in a stock pot (Note: This should be a full, bone in turkey breast). Add enough water to cover, salt, and maple syrup to make the brine. Cover and place under refrigeration for 36 to 48 hours.

Take the breast out and rinse it under cold water very thoroughly. Pat dry. Spritz the outside of the breast with a light coating of olive oil. Season with Poultry Perfect Rub (Big Oven recipe #161462) for best results or you can just make a simple rub of salt, pepper, and commercially available poultry seasoning. Take a bamboo skewer and make a kaboob of the onion, carrot, and lemon and then stuff it into the cavity of the breast. Slide the sprigs of thyme in also.

Prepare a bed of hot lump charcoal in your smoker and bring the temperature to 250 f.

Place the breast on the grate, bone side up (would be 'face down' if it were a whole bird). Add a handful of apple wood chips to the firebox about every 20 to 30 minutes to keep a nice flow of smoke. Replinish coal as necessary to maintain temp.

Smoke the bird until it hits 160 degrees internal (about 1 hour a pound at this temp). Remove from smoker, wrap with foil and place in an empty cooler (no ice) to let it rest for 30 minutes.

Slice and serve.