In a small Mixing Bowl, combine all spice rub ingredients — 2 tbsp 红糖 紧压, 1 tbsp 烟熏辣椒粉, 1 tbsp 粗海盐, 1 tbsp 粗海盐, 1 tsp 大蒜粉, 1 tsp 洋葱粉, ½ tsp 卡宴辣椒, ½ tsp 干牛至, and ½ tsp 干芥末粉. Mix well until fully blended.

Pat the 1 only 整只鸡 3.5–4.5 lbs，擦干 completely dry with paper towels — this is key for a good bark (crust). Rub the 2 tbsp 橄榄油 all over the outside of the bird and under the skin of the breast if possible. Coat the 1 only 整只鸡 3.5–4.5 lbs，擦干 generously with the spice rub on all sides, including the cavity. For best results, let the seasoned 1 only 整只鸡 3.5–4.5 lbs，擦干 rest uncovered in the Refrigerator for at least 1 hour (or overnight).

Set up your Grill or Smoker for indirect, low heat at 225–250°F. For a charcoal grill, bank coals to one side and place a drip pan with a little water on the other side. For a gas grill, only light one or two burners on one side. Add your soaked Wood Chunks or Chips directly to the coals or to a smoker box for gas grills.

Place the 1 only 整只鸡 3.5–4.5 lbs，擦干 breast-side up on the indirect heat side of the Grill (over the drip pan, not the coals). Close the lid and maintain a steady temperature of 225–250°F throughout the cook. Avoid opening the lid frequently — every peek adds time.

Smoke the 1 only 整只鸡 3.5–4.5 lbs，擦干 for approximately 2.5 to 3 hours, replenishing Wood Chunks or Chips and charcoal as needed to maintain temperature and smoke. The 1 only 整只鸡 3.5–4.5 lbs，擦干 is done when an instant-read Meat Thermometer inserted into the thickest part of the thigh (not touching bone) reads 165°F. The skin should be a deep mahogany color.

While the 1 only 整只鸡 3.5–4.5 lbs，擦干 smokes, combine 1 cup 烧烤酱 您最喜欢的品牌或自制, 1 tbsp 苹果醋, 1 tbsp 蜂蜜, and ½ tsp 辣酱 可选，增加辛辣感 (if using) in a small Saucepan over low heat. Stir and warm for 3–4 minutes until slightly thinned and glossy. Remove from heat and set aside.

When the 1 only 整只鸡 3.5–4.5 lbs，擦干 reaches an internal temp of 155°F (about 30 minutes before it's done), brush the glaze generously all over the bird. Close the lid and let the glaze set and caramelize as the 1 only 整只鸡 3.5–4.5 lbs，擦干 finishes cooking to 165°F. You can apply a second coat of glaze in the last 10 minutes for extra lacquer.

Once the 1 only 整只鸡 3.5–4.5 lbs，擦干 hits 165°F, transfer it to a Cutting Board and tent loosely with Aluminum Foil. Let it rest for 10–15 minutes — this allows the juices to redistribute and makes for a much juicier bird. Carve and serve with extra 1 cup 烧烤酱 您最喜欢的品牌或自制 on the side.