Lay the chicken on a plastic cutting board, breast-side up, with the neck facing you. Remove both wings at the joint between the wing and drumette. Remove the thigh quarters by slicing down on either side of the back end of the breast. Grab both legs, pop the joints that connect to the back, and turn the bird over. Remove the thighs and legs by slicing where they attach to the backbone. Hold the thigh and leg together, feel for the slight indentation where the joints meet and make an incision at this joint. Set the leg and thigh down and slice to separate. Repeat with the other leg piece. Turn the bird back over, breast-side up, put your knife against the breastbone and slice down along the rib cage, cutting the breast meat away from the bone. Be sure to include the drumette when removing the breast. Repeat on the other breast. Freeze the carcass for making stock.
Put the chicken pieces in a 1-gallon resealable plastic bag with the water, honey, and salt. Seal the bag and move around vigorously for 1 to 2 minutes to distribute the honey and dissolve the salt. Set the bag in a leak-proof container and refrigerate for 1 1/2 hours.
Meanwhile, combine the curry powder, chili powder, cocoa powder, adobo powder, cumin, and hot smoked paprika in another 1 gallon resealable bag.
Pat the chicken with paper towels until very dry. Do not rinse.
Put the chicken in the bag with the spice mixture and shake to thoroughly coat the chicken. Lay the pieces on a cooling rack set inside a half-sheet pan. Rest for 30 minutes.
Spritz 2 pieces of newspaper lightly with vegetable oil and put in the bottom of a charcoal chimney starter. Fill the chimney starter with natural chunk charcoal, 2 to 3 pounds, and set on the charcoal grate of a kettle grill until hot and ashy, 15 to 20 minutes. Prepare a ring of heavy-duty aluminum foil with the center 9 inches in diameter. Put this ring over the chimney starter and lay on the charcoal grate.
Carefully and evenly distribute the hot charcoal outside the ring. Set an aluminum pie pan in the center of the ring to catch any drippings. Set the cooking grate in place and heat for 2 to 3 minutes.
Lightly oil the cooking grate. Arrange the chicken pieces, skin-side down, on the grate over the hot coals. Turn the legs a quarter turn every 3 to 4 minutes. Turn the thighs, wings, and breasts after 4 to 5 minutes. Skin should blister and darken in color. Adjust intensity of heat by turning the grill grate to expose chicken pieces to cooler or hotter coals as needed and to avoid flare-ups.
After 9 to 10 minutes total cook time, move the breast to the center of the grill and cover with a second aluminum pie pan. After 1 more minute, put the wings on top of the pie pan. Lean the thighs and legs against the side of the aluminum pie pan away from the direct heat of the coals. Turn every 2 minutes. Put any pieces that finish cooking on top of the pan. After 18 to 20 minutes total cook time, check the temperature with an instant-read thermometer inserted in the deepest part of each piece. The pieces should reach 155ºF.
Remove the chicken to a clean, medium-sized bowl. Cover with a tea towel and rest 5 minutes. Transfer to a serving platter and serve immediately