Preheat the oven to 450ºF with rack in center.
Remove the giblets from the chicken then trim the excess fat from around the chicken cavity then rinse and thoroughly dry the chicken. (The drier the chicken, the crispier the skin.) Place the chicken in a roasting pan, baking dish or cast iron skillet.
Melt the butter with the garlic in a small saucepan over medium-low heat. Brush the melted garlic butter all over the chicken. Season the chicken liberally all over (including inside the cavity) with salt and pepper. Place the two lemon halves and the sprigs of rosemary inside the cavity.
Tie the legs together with kitchen twine. (Keep it simple with a loop around each leg and knotted in the center.)
Roast the chicken for about 1 hour, basting it every 15 minutes by using a spoon and tilting the pan to collect the juices then spooning them atop the chicken, until the internal temperature reaches 165ºF. (When testing the temperature with a meat thermometer, insert it into the breast but do not touch the bone for the most accurate reading.) Rotate the pan after every time you baste the chicken to guarantee even cooking.
Remove the chicken from the oven and transfer it to a cutting board. Allow the chicken to rest for 10 minutes before slicing and serving.