We start by making a wet brine. To do this, boil water, kosher salt, brown sugar and peppercorns. Once the salt and sugar dissolve, add cold water to cool.
When the water is at least room temperature and no cooler, submerge the turkey legs. Place in the refrigerator to brine.
Remove legs from brine, rinse and pat dry. Stir together the spices. Rub all over the turkey legs to season well.
Place the turkey legs in a 250-degree F smoker with a water pan. Insert a leave-in meat thermometer in the thickest part of the meat. Close the lid.
When the turkey legs reach an internal temperature of 120-130 degrees F, brush with olive oil. Close the lid again and continue to smoke until the turkey reaches 180 degrees F.