Cut the backbone out of the chicken and split the chicken in half. Pat dry with paper towels then season with salt on all sides. Place the chicken halves, skin side up, on a wire rack and into the fridge uncovered, overnight. Note: if in a rush, you can salt the chicken and roast on the same day.
Preheat oven to 500°F and set the rack to the middle level.
Remove the chicken from the fridge 1 hour prior to roasting.
Whisk together all of the sauce ingredients and taste test. Season with more salt and pepper as required. Set aside.
Place the chicken halves into a large 14-inch oven safe pan or large roasting pan. Drizzle the olive oil all over the chicken and season with black pepper. Pour 1 cup of chicken stock into the bottom of the pan and roast the chicken for 25 minutes.
Remove the chicken halves to a cutting board and cut into 6 pieces per half chicken for a total of 12 pieces. Pour out all but 1/3 cup liquid from the pan and place the chicken pieces back into the pan, skin side up. Pour the lemon sauce all over the chicken and into the pan.
Turn the low broiler on and once hot place the chicken on the middle rack to finish cooking. After 10 minutes the chicken should be well charred and crisp and completely cooked. Check that the pieces register at least 160°F internal temp. Note: If you like, the legs and thighs can be roasted for an additional 5-10 minutes at 500°F until they reach an internal temperature of 185°F or higher.
Place the chicken in a platter and whisk the cold butter into the pan sauce. Mix in the parsley then pour the sauce over the chicken. Top with the lemon zest and serve with crusty bread to mop up the sauce. Enjoy!