Set up your grill for indirect cooking and preheat to 300 degrees. Place a drip pan under the grate and add 1 cup water or chicken broth and half the onion to the pan.
Remove the turkey from the brine, rinse and pat dry. Insert the other half of the onion in the cavity of the turkey, and rub the outside of the bird with vegetable oil.
Sprinkle Fin & Feather BBQ Rub over both sides of the turkey. I like to use a small hand strainer to get a nice even coating all over the bird. Use 1-2 tablespoons for a smaller turkey and 2-3 tablespoons for a larger one, reserving 1 tablespoon for finishing.
Place the turkey on an oiled grate and close the lid. Total cooking time will vary depending on the size of the turkey, 4-6 hours for a 10-12 pound turkey and up to 10 for a really large 25 pound bird.
Begin by cooking the turkey several hours, attentively maintaining the temperature of your grill. Meanwhile, melt the butter with the remaining tablespoon of Fin & Feather BBQ Rub, and set aside.
After the turkey has been on for at least 3 hours, open the grill and, working quickly, baste the turkey with the melted spice butter using the sage bundle as a brush. If your drip pan is dry, add more water or chicken broth. Check the temperature and close the lid. The turkey won't be done at this point but the temperature will give you an idea of how fast it is cooking.
Continue cooking until the internal temperature at the thickest part of the thigh reaches 170 degrees. When you open the grill to check the temperature, baste the turkey and add liquid to the drip pan as needed.
Carefully remove the turkey from the grill and allow it to rest 10-15 minutes before carving. Use the drippings to make your favorite gravy.
Notes:
Make sure the turkey you buy will fit on your grill with the lid closed. I've had some close calls on this one! An internal meat thermometer is a great tool to have. You can monitor the temperature of the meat without opening and closing the lid. This takes the guesswork out of when to check the temperature. It is fine to increase the grill temperature over the 300 degrees suggested here. Some like to cook at 325 or even 350 to reduce the cooking time, just be sure to take the turkey to a safe internal temperature before eating. When using charcoal, account for the fact that in November it is pretty cold in most places. That means it will take more fuel overall to keep your grill at temperature.