Early on the day you want to serve, place the chicken on cutting board breast-side down. Use kitchen shears to cut down the ribs on one side of the backbone 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!
Place the chicken on an oven-safe wire rack set inside a half sheet pan. Rub the chicken on both sides with 2 tablespoons of the salt. Flip skin-side up, then refrigerate, uncovered, for 8 to 12 hours.
About 2 hours before you’re ready to serve, place a rack in the top of the oven and place the pizza stone(s) on it (see note). Place another rack 6 inches below the top rack, then crank the oven to 500°F. Give the oven and stone(s) at least an hour to come up to temperature. Your patience will be rewarded.
While the oven is heating, remove the chicken from the refrigerator and let sit on to counter at room temperature.
After an hour of oven heating time, combine the butter, Aleppo pepper and za'atar in a heavy metal measuring cup or small saucepan, place over low heat, and cook, stirring occasionally, until the butter is red and fragrant, about 5 minutes.
Flip the chicken skin-side down and brush with half the butter mixture. Transfer to the oven rack below the stones and roast the bird for 10 minutes.
Carefully remove the pan with the chicken, flip the bird skin-side up, and brush the skin with the remaining butter mixture. Insert a remote probe thermometer into the breast and set the alarm to 160°F. Return to the oven and continue to roast until the alarm sounds, about 25 minutes later.
Remove the chicken to a cutting board and let rest for 10 to 15 minutes. Carve and serve.