THAW THE TURKEY if it is still frozen. This can take days. See notes.
1 to 3 days before smoking: Remove the neck and giblets from the turkey (discard or save for gravy). With paper towels, pat the turkey dry. You do not need to rinse the turkey.
Mix up the brine: Add the dry brine ingredients to a small bowl. Stir to combine. Rub all over the bird, including inside the cavity. Place the turkey on a rimmed baking sheet. If cooking within 24 hours, leave it uncovered and refrigerate; if cooking in 2 to 3 days, cover with plastic, then refrigerate for up to 3 days total.
About 24 hours before smoking: Uncover the turkey, then return to the refrigerator. This step dries the skin, which helps it crisp.
1 hour before smoking: Remove the turkey from the refrigerator and let stand at room temperature.
Heat your smoker to 325°F. We’ll be cooking over indirect heat.
Cut the carrots into 1-inch pieces (if your carrots are very thick, halve them lengthwise first). Cut the apple, onion, and lemon into eights. Cut the head of garlic in half crosswise (that's horizontally through the cloves), then break each half into a few big pieces. No need to peel or core any of these; they’re just for flavor.
Stuff the turkey cavity with the thyme and a mixture of the carrots, apples, onion, lemon, and garlic. Scatter the remaining carrots, apple, onion, lemon, and garlic in the bottom of a large disposable aluminum roasting pan.
Tuck the turkey's wings: Stretch them upwards, then tuck them under the turkey's body (as if the turkey were reaching its wings up and behind its neck). Tie the legs snugly together with kitchen twine (or in desperate times, a rope of aluminum foil).
Set a rack in the roasting pan, then place the turkey on top. Brush the turkey all over with the melted butter. Sprinkle with black pepper.
If you have a meat probe, insert it in the thickest part of the thigh without it touching bone (a digital one with an alarm set to 160°F is ideal). Set the Turkey on the smoker, then pour in the apple juice.
Smoke the turkey for 10 to 12 minutes per pound—a 12- to 14-pound turkey will need 2 to 3 hours roasting time), until the thigh registers at least 160°F and up to 180°F and the breast is at least 150°F (and no more than 165°F) on an instant read thermometer inserted in the thickest part of the meat without the thermometer touching bone or being in the empty turkey cavity - per the FDA turkey is considered cooked at 165 degrees F, but its temperature will rise as it rests. DO NOT OVERCOOK THE TURKEY. Check the turkey early to be safe, and see How Long to Cook a Turkey for more information.
Let the turkey rest (mandatory!): Transfer the turkey to a cutting board. Cover and let rest for at least 20 to 30 minutes (it will stay piping hot much longer; don’t worry about it getting cold).
Carve the turkey and serve with the pan juices and/or gravy. WAY TO GO!
Notes
*Make sure your turkey is NOT already brined. If it does come pre-brined (many Butterball turkeys do come already injected), brine it for 24 hours instead of 48 hours. Kosher turkeys do not need to be brined.
THAWING: For every 5 pounds of turkey, plan on 24 hours thawing in the refrigerator (that's 3 days thawing for a 15-pound bird). For emergency fast thawing, place the turkey in a cold water bath and change the water every 30 minutes. This will still take about 8 hours for a 15-pound turkey. In an ideal world, purchase your turkey fresh from a local butcher. That way you can avoid this time-consuming (and refrigerator hogging) step entirely. You also can thaw turkey in a cooler, provided it is kept below 40 degrees F. Bird sizes: When possible, try not to purchase a bird that's larger than 16 pounds—their proportions make it much more difficult to get juicy meat throughout. If you are cooking for a large crowd or want a lot of leftovers, cook two smaller birds instead.
A NOTE ON TIMING: A LOT will affect how long it takes your turkey to cook—how consistent the temp of your smoker stays, the type of turkey you bought, the temperature outside…I could go on! Plan on buffer time on either end.
TO STORE: Refrigerate leftover smoked turkey in an airtight storage container or ziptop bag for up to 4 days. To keep the meat moist, drizzle some of the turkey pan drippings or chicken broth over the top before refrigerating it.
TO REHEAT: Wrap the smoked turkey in an aluminum foil pouch, drizzle turkey drippings or broth over the meat, then seal it. Warm the pouch in a baking dish in a 300 degrees F oven.
TO FREEZE: Freeze turkey in an airtight freezer-safe storage container for up to 3 months. Let it thaw overnight in the refrigerator before reheating according to the instructions above.