Step 1Remove the giblets and neck from the turkey and either discard or reserve for another use. Rinse the turkey well, inside and out, and pat dry.
Step 2At least 12 hours before cooking, combine the salt, sugar, thyme, allspice and cayenne and mix well. Rub the mixture all over the skin of the turkey. Place the turkey in a shallow dish, cover with plastic wrap and refrigerate overnight. Remove it from the refrigerator 1 hour before roasting.
Step 3Heat the oven to 500 degrees. If the turkey has been salt-cured, rinse it and wipe dry. Place the turkey in a roasting pan. Fill the body and neck cavities loosely with focaccia stuffing (bake any leftover stuffing separately). Rub the turkey all over with the olive oil and season it with black pepper.
Step 4Roast 15 minutes, then lower the oven setting to 350 degrees. Roast until a thermometer inserted into the thickest part of thigh or breast registers 165 degrees, or until juices run clear, about 2 1/2 hours. Baste if you like, but it's not necessary. If the breast skin starts to darken too much or the stuffing starts to burn, cover loosely with foil.
Step 5Place the turkey pan on a trivet. Scoop out the stuffing and transfer to a bowl. Cover the bowl and keep warm. Loosely cover the turkey with foil and let it stand 30 minutes before carving.