The day before: remove the giblets and neck from the cavity. Trim the loose flaps of skin and any large lumps of fat around the cavity opening.
Pat the duck completely dry with paper towels, inside and out.
Prick the skin all over at a slight angle, especially where it is thickest on the breast, thighs, and around the legs. Do not pierce the meat. Scoring the breast skin in a diamond pattern is optional.
Mix the salt, pepper, and spice. Rub the mixture over the skin and into the cavity.
Set the duck breast-side up on a rack over a tray and leave it uncovered in the refrigerator for 12 to 24 hours.
Roasting day: take the duck out of the refrigerator 30 to 45 minutes before roasting. Preheat the oven to 325°F (165°C) with a rack in the lower third.
Put the orange quarters, garlic, and thyme in the cavity and tuck the wing tips under. Set the duck breast-side up on a rack in a roasting pan.
Roast for 1 hour 30 minutes. Carefully spoon off the fat from the pan, and prick the skin again, especially around the thighs.
Roast another 30 minutes, then drain the fat again.
Raise the oven to 425°F (220°C). Roast for 20 to 30 minutes until the skin is deep golden and crisp. If using the glaze, brush it on only during the last 8 to 10 minutes.
Check that the thickest part of the thigh reads at least 165°F (74°C). Start checking after about 2 hours of total roasting time.
Rest the duck on a cutting board, loosely tented, for 15 to 20 minutes. Do not wrap it tightly in foil.
Carve off the legs, remove each breast whole, and slice crosswise. Serve right away.