The spices here form the basis for a classic dry barbecue rub, but if you don’t have one or two of them, simply leave them out — the chicken will still taste great. The salt is the only important seasoning here, as it helps draw out moisture from the skin, getting it extra-crisp in the oven. Try your best to find a chicken that’s at least 4 pounds (the average of what I find in grocery stores); if the chicken you get is larger or smaller, adjust the cooking time accordingly.
In a small bowl, stir together the salt, paprika, oregano, pepper, garlic and onion powders, thyme, cumin and cayenne. Measure out 3 tablespoons of the spice mixture and reserve it in another bowl. Place a sheet of foil to the side.
Working on a large rimmed baking sheet, use kitchen shears to cut along each side of the chicken’s backbone and remove it. Turn the chicken breast side up and press on the breastbone to flatten the chicken. Sprinkle the larger amount of spice mixture evenly over both sides of the chicken, rubbing it into the meat and skin until well coated. Transfer the chicken skin side up to the sheet of foil, sprinkle evenly with 1 tablespoon of the reserved spice mixture and let stand at room temperature until the oven is heated.
Wash your hands, then use the paper towel you dried them with to wipe the baking sheet clean. Pour the oil in the baking sheet, tilting the baking sheet so the oil covers the bottom of it evenly, then place the baking sheet in the oven. Heat the oven to 425 degrees.
Once the oven is heated, open the door and pull out the rack with the hot baking sheet. Pick up the chicken and lay it skin side down on the sheet. Immediately sprinkle another 1 tablespoon reserved spice mixture over the side facing up. Close the oven and cook until the skin has rendered most of its fat, about 20 minutes.
Open the oven, then use two pairs of tongs (or folded paper towels grasped in your fingers) to flip the chicken skin side up. Close the oven and continue roasting until the chicken is cooked through and the skin is crisp all over, 30 to 40 minutes more.
Remove the baking sheet from the oven and immediately sprinkle the remaining 1 tablespoon reserved spice mixture evenly over the chicken. Tent the chicken loosely with foil and let stand for 15 minutes. Serve from the baking sheet so you can sop up all its juices and spices with bread or rice.
When the chicken has cooked for 50 minutes, brush the chicken with a layer of your favorite barbecue sauce to cover, then repeat every 3 minutes until the chicken is done, for a total of 4 layers of sauce.
Instead of heating the oven, prepare a charcoal or gas grill for indirect grilling and brush the grill grates with some oil. Lay the chicken skin side down on the direct heat part of the grill and immediately sprinkle another 1 tablespoon reserved spice mixture over the side facing up. Close the grill and cook until the skin has rendered most of its fat and is golden brown, 15 to 20 minutes. Open the grill, then use two pairs of tongs (or folded paper towels grasped in your fingers) to flip the chicken skin side up and position it over the indirect side of the grill. Close the grill and continue roasting until the chicken is cooked through, the skin is crisp all over and an instant-read thermometer inserted in the thigh reads at least 190 degrees, 30 to 40 minutes more. Transfer the chicken to a cutting board and immediately sprinkle the remaining 1 tablespoon reserved spice mixture evenly over the chicken. Tent the chicken loosely with foil and let stand for 15 minutes before serving.
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