Directions:

1. Place salt in a large bowl or Dutch oven; add a little water and stir until salt is dissolved. Place chicken in salt water brine; add enough water to cover chicken. Refrigerate up to 4 hours.
2. Remove chicken from brine, drain, and pat dry with paper towels. Place chicken, breast-side down, on a clean cutting board.
3. Cut along both sides of chicken backbone using kitchen shears. Remove bone; reserve for another use or discard. Maintain skin-side down position; cut into breast bone and a bit of the cartilage above the bone about 1/4-inch deep using the tip of a sharp knife. Flip chicken skin-side up.
4. Place the heel of one hand on top of other hand's wrist; press down on the center of the breast using the heel of the hand on top of the cut area to flatten the center and achieve a more uniform thickness.
5. Combine smoked paprika, garlic powder, cumin, and black pepper in a small bowl; rub onto both sides of chicken, gently lifting the skin wherever possible to place some rub directly onto meat. Refrigerate seasoned chicken uncovered for at least 2 hours.
6. Remove chicken from the refrigerator before grilling so it can come to room temperature for 10 to 15 minutes.
7. Preheat an outdoor grill for medium heat to about 375 degrees F (190 degrees C) and lightly oil the grate.
8. Place chicken, bone-side down, onto the preheated grill and cook for 50 to 60 minutes. An instant-read thermometer inserted near but not touching the bone should read 150 degrees F (65 degrees C). Flip chicken, skin-side up; brush with barbecue sauce. Continue grilling until chicken is no longer pink at the bone and the juices run clear, about 20 minutes more. An instant-read thermometer inserted near but not touching the bone should read 165 degrees F (74 degrees C).
9. Transfer chicken to a platter, tent with foil, and rest for about 10 minutes. Cut into 6 servings. Serve with additional barbecue sauce.