Prepare turkey for brine by fully defrosting, and removing giblets, neck, and trimming off excess fat.
In a large stock pot over medium-high heat, combine water, salt, sugar, and bourbon. Bring heat up and dissolve the salt and sugar into the liquid, then turn off heat.
Let cool and then add remaining brine ingredients. Add turkey to brine and cover. Brine for 24 hours, avoid going beyond 30 hours. At a minimum brine for four.
Add herbs to room temperature butter and combine. Be sure when you are using for the turkey, it is still room temperature.
Preheat Smoker to 275 degrees.
Remove turkey from brine and rinse. Pat dry with a towel and let completely dry, can add back to fridge as well for an hour to help. You want a dry bird for the dry rub.
Stuff cavity of the bird with thyme, rosemary, oranges, lemons, and garlic. Then stuff butter between the skin and breasts, spreading it out with your hands all along the breast.
Coat liberally with olive oil and then dry rub. Season the bottom as well. Tie up legs and wings with kitchen string, or tuck them to keep tight against the turkey.
Place turkey on the smoker, and insert your digital meat probe into the breast and thigh or leg. Smoke until the internal temperature of both reads 165 degrees (F). Use an instant read to check temp in various part of the turkey, even if the digital probes read 165 to confirm all parts of the turkey are cooked through.
Remove from smoker (will likely take 3 hours with a 12 - 14 pound bird) and cover with foil. Let cool for about 20 minutes. Then slice and serve.