Special equipment: Special Hardware: heavy duty kitchen shears, one 2-gallon zip-top storage bag, pizza stone(s)*, an ordinary household oscillating or box-style fan, remote probe thermometer
Place chicken on cutting board breast-side down. Use kitchen shears to cut down the ribs on one side of the back bone and then the other and remove. Open the bird like a book and remove the keel bone separating the breast halves by slicing through the thin membrane covering it (I like a thin paring knife for this), then work two fingers under the bone and lever it out. Flip chicken breast-side up and flatten it, pulling the legs toward you, so that the bird looks like a big, meaty butterfly.
Now wash those chicken-y hands!
Secure a 2-gallon zip-top bag in a small pot or storage container and pour in the hot water followed by the salt. Stir until the salt dissolves then add the ice and then the chicken to the bag, seal tightly and refrigerate 8 to 12 hours.
After brining, remove bird from bag, drain thoroughly and place on a rack set inside a sheet pan. Dry with paper towels and smooth the skin to cover any exposed meat then park the pan in front of a fan (medium speed will do) until the skin feels dry and tight and slightly leathery. A typical broiler/fryer will take two hours depending on humidity.
Place a rack in the top of the oven and place the pizza stone(s) on it. Place another rack 6 inches below the top rack then crank the oven to 550 degrees F. Give the oven and stone(s) at least an hour to come up to temperature. Your patience will be rewarded.
Combine the butter, Aleppo pepper and za'atar in a heavy metal measuring cup and cook over low heat for 5 minutes or until the butter is red and fragrant.
Flip chicken skin-side down, brush with half the butter mixture and season with 1/2 teaspoon of salt.
Pour one cup of water into the pan (to help minimize the smoke produced from the drippings) and place the pan on the rack below the stones and cook the bird for 10 minutes.
Carefully (but quickly) slide out rack, flip the bird skin-side up, brush the skin with the remaining butter mixture and season with the remaining 1/2 teaspoon salt. Insert a remote probe thermometer into the breast and set the alarm to 160 degrees F. Now close the door!
When the alarm sounds (about 25 minutes later) turn the oven off and reset the alarm to 165 degree F. Then remove the chicken and rest 10 to 15 minutes before carving.
*Although plenty of folks use large, single pizza stones I prefer smaller, thicker stones that can be arranged in various patterns in the oven. Most sets that I've used have come with 5 stones that can be arranged differently to suit various oven shapes and sizes. Smaller stones, in my experience, tend to break less often. But that's just me.