• Chicken:
1 cup salt
2 (4-pound) whole chickens, giblets discarded (We prefer to halve the chickens ourselves, but you may be able to buy halved chickens from your butcher.)
Pepper
2 cups wood chips, soaked in water for 15 minutes and drained
• Sauce:
2 teaspoons vegetable oil
1 onion, chopped fine
4 cups chicken broth
1 1/4 cups cider vinegar
1 cup brewed coffee
3/4 cup molasses
1/2 cup tomato paste
1/2 cup ketchup
2 tablespoons brown mustard
1 tablespoon hot sauce
1/2 teaspoon garlic powder
1/4 teaspoon liquid smoke
Dissolve salt in 4 quarts cold water in large container. Remove backbones from chickens and split chickens in half lengthwise through center of breastbone. Using metal skewer, poke 20 holes all over each chicken half. Submerge chicken halves in brine, cover, and refrigerate for 1 hour. Remove chicken halves from brine, pat dry with paper towels, and season with pepper. Using large piece of heavy-duty aluminum foil, wrap soaked wood chips in foil packet and cut several vent holes in top.
Meanwhile, heat oil in Dutch oven over medium-high heat until shimmering. Add onion and cook until softened, about 5 minutes. Whisk in broth, vinegar, coffee, molasses, tomato paste, ketchup, mustard, hot sauce, and garlic powder and bring to boil. Reduce heat to medium-low and simmer until mixture is thick and reduced to 4 cups, about 65 to 75 minutes. Stir in liquid smoke; reserve 1 cup sauce for serving. (Sauce can be refrigerated for up to 2 days.)
• For a charcoal grill: Open bottom vent halfway. Light large chimney starter filled with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour into steeply banked pile against side of grill. Place wood chip packet on coals. Set cooking grate in place, cover, and open lid vent halfway. Heat grill until hot and wood chips are smoking, about 5 minutes.