Preheat your barbeque to medium-high. Coat and rub the turkey with the barbecue spice. Set the turkey, skin-side up, on one side of the barbecue. Close the lid. Turn the heat off underneath the turkey; leave the other side of the barbecue set to medium-high. Barbecue the turkey 45 to 55 minutes, or until its temperature in the centre of the thigh or breast registers 170 degrees F on an instant read meat thermometer. Rest the turkey 10 minutes and then thinly slice the meat. Spread the buns with mayonnaise. Set a piece of lettuce on each bun. Mound an equal amount of turkey on each bun. Drizzle the meat with barbecue sauce; top with the onions and pickles and serve.
Note: You can use a store-bought barbecue spice rub or make your own by combining 1/2 tsp. ground cumin, 1/2 tsp. chili powder, 1/2 tsp. ground sage, 1/2 tsp. salt, 1/2 tsp. freshly ground black pepper, 1/4 tsp. paprika, and 1/8 tsp. cayenne pepper.