In a large pot, stir together 10 cups water, salt, allspice, cloves, bay leaves, thyme, rosemary, sage, and onion. Bring the mixture to a boil, then remove from heat. Pour in beer and ice. 

Allow the brine liquid to cool completely to room temperature. 

Rinse your turkey and remove the bag of innards that are tucked inside. Place the turkey into whatever you plan to brine it in. I used a giant stock pot that fits a 13-lb turkey, but you can also use a food-grade safe bucket or oven bags. 

Pour the brine over the turkey and cover. Place in the refrigerator. 

Brine your turkey for 16 to 18 hours, rotating every 6 to 8 hours if your turkey is not completely covered in the brine. 

Remove from fridge and remove the turkey from the brine. Truss the legs and tuck the wing tips back around the bird. Rub the bird all over with olive oil. Season with a small amount of black pepper.

Set your smoker to smoke at 225 degrees F and preheat with the lid closed for 10 to 15 minutes. 

Place the turkey on a roasting rack set inside a roasting pan. Place the pan directly on the grill grate or directly in your smoker, depending on the model you are using. Cook until the internal temperature reaches 100 to 110 degrees F. This took me about 2 1/2 hours for a 13+lb bird. It should take between 1 1/2 to 3 hours depending on the size of the turkey. 

Increase temperature to 350 degrees F. This will take another 1 1/2 to 3 hours, depending on turkey size. Continue to cook until a meat thermometer registers 160 degrees F when inserted into the thickest part of the breast. 

Remove the roasting pan from the grill and let rest 15 minutes until the turkey is 165 degrees F before carving.