To make smoked turkey drumsticks, brush the drumsticks with olive oil; sprinkle them with barbecue seasoning; smoke the turkey using heated, foil-covered wood chips for three and a half hours; direct heat at the turkey; and let it cook for up to seven minutes until crispy. The recipe serves four people.
Preheat a gas grill to 250 degrees Fahrenheit. Soak 3 cups of hickory wood chips as directed on the package, and drain them. On heavy-duty foil, place the wood chips, and fold up all ends, making sure to enclose the chips. Poke holes onto the foil using a knife, and heat them for 30 minutes or until they start smoking. Turn off one side of the grill for indirect heating.
Using a paper towel, pat the turkey, brush it with 3 tablespoons of olive oil, and season it with 3 tablespoons of barbecue seasoning. Place the wood chips and turkey onto the non-heated grill side, and smoke the turkey for up to three and a half hours, turning three to four times until the turkey juice is clear when the thickest part is bone-cut. The grill should be at 165 F.
Place the turkey on the direct-heat side of the grill, and increase the heat to 350 F. Cook the turkey for up to seven minutes while turning two to three times until slightly crisp.