Preheat your smoker to 325°F using your favorite hardwood. Maple, pecan, alder or apple are all great choices for smoking turkey.
In a small food processor or coffee grinder, add the salt, sugar, black pepper, thyme, sage, rosemary, garlic powder, onion powder, bay leaves and lemon zest. Pulse for about 10 seconds, until everything is combined. Set aside.
Spatchcock the turkey by removing the giblets, neck and any plastic hardware. Place the turkey on a cutting board with the backbone facing up. Use kitchen shears and cut along both sides of the backbone to remove it. Turn breast side up and press down to flatten it.
Gently use your fingers to separate the skin from the breast and thigh meat. Place 2 tablespoons of the butter under the skin on the first breast and then do the same with the other breast. Add 2 tablespoons of butter to each thigh until all the butter is distributed beneath the skin of your turkey.
Place the turkey breast-side down on your work surface and drizzle with 2 tablespoons of olive oil. Rub the oil over the surface, then season with about one third of the herb mixture. Flip the turkey breast-side up, drizzle with the remaining olive oil, and season with the remaining herb mixture.
Smoke the turkey for about 2 hours or cook until internal the temperature reaches 165°F in the thickest part of the breast. Let rest for 15 minutes before slicing.