Build the brine: In a large pot, squeeze the lemon halves and drop them in along with the ginger, salt, sugar, thyme, onion quarters, peppercorns and 8 cups of water. Bring to a boil while stirring to dissolve the sugar and salt then lower to a simmer until the ginger is tender and the pot is fragrant, about 15-20 minutes. Remove from the heat and pour in the remaining 4 cups of ice water. Pour into a brining bag and allow to cool slightly.

Remove the neck bone and gizzards from the turkey, refrigerate both to use for gravy or rice. Add the turkey to the brining bag and press all of the air out then seal. Refrigerate 24 hours (not just overnight).

Remove turkey from the brine and pat dry. Butterfly the turkey by cutting out the backbone, then the breast plate – save all the bones for gravy, stock or rice. Pat skin dry again then rub with olive oil all over. Season skin with salt and pepper generously. Place the turkey skin-side up in a roasting pan with the legs overlapping on the top of the body. Leave at room temperature for 2 hours.

Heat grill to 450ºF. (If using coals, about 5 pounds works, think about using a coal warmer to replenish during grilling. Also move coals to the edge once ready and put a drip pan in the center). Place turkey as rested, legs overlapped and skin-side up, over indirect heat and close grill. Cook until internal temperature between the leg and body is 155ºF degrees, about 1 1/2 to 2 hours. If using gas, allow the temperature to rest between 325ºF-350ºF during grilling time. With coals, the temperature will naturally fall. Replenish with hot coals if the temperature falls below 300ºF.