The day before you wish to eat the chicken, take it out of the fridge (thaw in the fridge for 2 days if it was frozen).
Remove any giblets left in the cavity of the chicken. Do not rinse the chicken.
place the chicken in a pan (I use a smaller rimmed baking sheet), pat dry with a paper towel, and rub the kosher salt all over the outside of the chicken.
put the salted chicken back in the fridge for 12-24 hours.
Make the compound butter by mixing the butter, garlic, lemon zest, rosemary and pepper in a small bowl. This can be done the day before and either be left on the counter or put in the fridge, just let it come up to room temperature before you take the chicken out of the fridge.
The next day, remove the chicken from the fridge. Place two baggies full of ice on the breasts, and let the legs come up to room temperature for about an hour.
Remove the ice packs.
Run your finger under the skin of the breasts and legs, creating pockets for the butter. There will probably be a membrane you will need to break through. This is normal, just be careful not to break the skin.
With your fingers, push as much compound butter as you can into the pockets you created under the skin.
Place chicken on a metal cooling rack sitting inside a rimmed baking sheet, oriented so the legs will be pointing to the back of the oven. This is usually the hottest part of the oven.
Preheat oven to 500 degrees.
Place your probe thermometer into the center of one of the chicken breasts.
Put the chicken in the oven, and immediately turn down the temperature to 350 degrees.
Bake until the thermometer registers 145 degrees in the breast.
Take the chicken out of the oven ad let rest for 30 minutes. The temperature should rise by 10-15 degrees. As long as it stays at or above 145 degrees for 9 minutes, it is safe to eat.
Carve and serve.