Make the spice rub:
In a small bowl, whisk together all of the ingredients and break up any lumps with your fingers.
Make the mop sauce:
In a medium bowl, whisk together all of the ingredients.
Make the barbecue sauce:
Melt the butter in a 1-quart saucepan over medium-low heat. Add the shallots and ginger and cook, stirring, until lightly browned, 3 to 4 minutes. Stir in the brown sugar, lemon juice, and mustard, increase the heat to medium, and simmer gently, whisking often, until the sauce has thickened, 4 to 6 minutes. Season to taste with salt and pepper.
Prepare the wood chips and chicken:
Put 1-1/2 cups of wood chips (preferably oak) in a large bowl and cover with water. Let soak for 30 minutes, then drain.
Put each chicken breast side down on a cutting board. Using kitchen shears or a sharp knife, cut out the backbones of the chickens (save for another use or discard). Open the chickens like a book and cut through the breast bones to separate the chickens into halves. Pat the chicken halves dry with paper towels. Using your hands, rub 1 Tbs. oil over the skin of each chicken half, then rub each half with a quarter of the spice rub. Let stand at room temperature while preparing the grill.
Prepare the grill:
Prepare a gas or charcoal grill fire for indirect grilling over medium heat (350°F).
If using a charcoal grill, bank the coals to one side. Put a 10x15-inch foil drip pan next to the coals and fill it halfway with water. Sprinkle the soaked wood chips over the coals. Replace the grill grate.
If using a gas grill, put a 10x15-inch foil drip pan on the inactive burners and fill it halfway with water. Use two layers of heavy-duty aluminum foil to make a V-shaped packet to hold the wood chips. Set the foil packet between the active burners. Sprinkle 1/2 cup of dry wood chips into the foil packet and let them ignite. Once they are smoking well, sprinkle a handful of the soaked chips over the dry chips to create even more smoke. Replace the grill grate.
Clean the grate with a wire brush and, using tongs, wipe the grate with a paper towel or cloth dipped in oil.
Smoke the chicken:
Put the chicken halves skin side up over the drip pan and cover the grill.
Smoke the chicken for 20 minutes, then use a heatproof barbecue mop or other brush to coat it with some of the mop sauce. Continue grilling the chicken, brushing with the mop sauce every 15 minutes, until an instant-read thermometer inserted into the thickest part of a thigh reads 160°F, about 45 minutes. During this time, switch positions of the chicken halves if they’re not cooking evenly, but do not flip. If using a gas grill, add more soaked chips through the grate as necessary to keep the smoke going. (Discard any remaining mop sauce.)
Continue to grill, covered (without adding more chips if using a gas grill), until the skin is deep golden-brown and an instant-read thermometer inserted into a thigh reads 170°F, 10 to 15 minutes more.
Brush the skin side of the chicken halves with all of the barbecue sauce. Using tongs, flip the chicken halves skin side down directly over the heat and cook until the sauce begins to sizzle and brown, 2 to 3 minutes.
Transfer the chicken halves to a platter and let rest for at least 5 minutes before serving.
Serve the chicken with Grilled Corn on the Cob, Traditional Cole Slaw, and your favorite potato salad.
nutrition information (per serving):
Photo: Scott Phillips