Use a sharp knife to make 2 or 3 short slashes in the skin of each piece of chicken, taking care not to cut into meat.

Combine the salt, sugar, and spices in a small bowl and mix thoroughly. Coat the chicken pieces with the spices, gently lifting the skin to distribute the spice rub underneath but leaving it attached to chicken. Transfer the chicken skin side up to wire rack set over rimmed foil-lined baking sheet, lightly tent with foil, and refrigerate 6 to 24 hours.

Secure the skin of each breast piece with 2 or 3 toothpicks placed near the edges of the skin.

Adjust an oven rack to the middle position; heat the oven to 425 degrees.

Roast the chicken until the thickest part of smallest piece registers 140 degrees on an instant-read thermometer, 15 to 20 minutes.

Increase the oven temperature to 500 degrees and continue roasting until the chicken is browned and crisp and the thickest parts of the breast pieces register 160 degrees, 5 to 8 minutes longer, removing pieces from the oven and transferring to a clean wire rack as they finish cooking. Continue to roast the thighs and/or drumsticks, if using, until the thickest part of the meat registers 170 to 175 degrees, about 5 minutes longer.

Remove from the oven; transfer the chicken to a rack and let it cool completely before refrigerating or serving.