Place a wire rack on top of a rimmed baking sheet. Liberally sprinkle salt all over the outside of the chicken. Cover the chicken loosely with parchment paper and refrigerate overnight (about 24 hours).
Preheat oven to 500° F. Let the chicken sit on the counter and come to room temperature for about 30 minutes before roasting.
In a large bowl, toss together the potatoes, 2 tablespoons of olive oil, and salt and pepper, to taste.
Place potatoes in the bottom of a cast iron Dutch oven. Add the lemon, garlic and onion. Drizzle with about 1 more tablespoon of olive oil. Place thyme and rosemary on top.
Place the chicken on top of the potatoes and herbs in the Dutch oven. Tie the legs of the chicken together and tuck the wings underneath. Brush with melted butter and season with pepper.
Roast chicken at 500° F for 20 minutes. Without opening the oven, reduce the temperature to 350° F and continue roasting for 30-40 more minutes, or until a meat thermometer reads 165° F when inserted between the thigh and breast.
Remove the chicken from the oven. Allow to rest for at least 10 minutes before carving and serving.
If you don't have 24 hours to chill the salted chicken, no problem! As little as 1 hour will still have an effect. If it's more convenient, you can chill the chicken in the salt brine for up to 72 hours.
Bring the chicken to room temperature for about 30 minutes before roasting in order to ensure even cooking.
Make sure that your chicken is very dry before roasting -- otherwise you'll end up steaming the bird for the first part of the cooking time (which makes it harder to achieve a crispy skin).
Cooking time will vary depending on the total weight of your chicken. Always use a meat thermometer to test the internal temperature of the meat to know when it's done.
Truss the chicken. This only takes a minute or two, but tying together the chicken legs with twine and tucking the wings underneath helps the chicken cook evenly.
Season liberally. Don't be shy with the salt. This is a big piece of meat, so you want to add plenty of flavor by using enough seasoning. Enough salt is also imperative for successful dry brining and crispy skin.
For the juiciest meat, allow the chicken to rest for at least 10 minutes before carving.
Don't omit the butter. The butter on the outside helps to make sure that the exterior is perfectly crispy and golden brown, and it also adds great flavor.