TO MAKE THE BRINE:
In a large stockpot, bring 6 quarts water, 1 1/2 cups salt, brown sugar, coriander, ginger, and bay leaves to a boil. Lower the heat and simmer 10 minutes, stirring occasionally to make sure the salt and sugar are dissolved. While the brine is simmering, fill a bucket (or pot) big enough to hold a turkey with the ice. Pour the brine over the ice. When the brine has cooled, add the turkey. Place a heavy object like a plate or lid on top of the turkey to keep it submerged in the liquid. Brine in the refrigerator for up to 8 hours.
TO MAKE THE SAUCE:
Heat the vinegar and granulated sugar in a medium saucepan over medium heat until the sugar dissolves. Turn off the heat, stir in the ketchup, honey, 1/4 cup salt, red pepper, and black pepper. Reserve 1 1/2 cups for passing at the table.
TO MAKE THE TURKEY:
Special equipment: 4 cups wood chips, such as hickory or mesquite, soaked in water for 30 minutes and drained
Prepare an outdoor grill with a medium-high fire for both direct and indirect grilling. Position a drip pan under the grate on the indirect side of the grill.
Sprinkle the cavity of the turkey with salt and stuff with the celery, lemons, onions, and parsley, then tie the legs. Place the turkey breast-side up over the drip pan.
Toss a cup of the soaked wood chips onto the coals. Cover the grill and rotate the lid so that the vent holes are directly over the meat. To maintain a medium-low smoky fire, add about a dozen pieces of charcoal and another cup of wood chips to the fire whenever the fire dies down. Rotate the turkey about every 45 minutes to prevent the side closest to the coals from overcooking.
After one hour, begin basting the turkey every 20 to 30 minutes with the remaining 2 1/2 cups of sauce. (Keep the grill covered between basting.) Cook until an instant-read thermometer inserted in the thigh, not touching the bone, registers 165 degrees F, 2 1/2 to 3 hours. Transfer to a cutting board and let rest 15 minutes before carving.