THE DAY BEFORE COOKING, WASH pig inside and out; soak it in very cold water with vinegar for a few hours. This freshens and whitens the meat. If you pig is frozen, it can also defrost during this soaking. Over a medium heat cook the carrots, celery and onions in the oil for a good 10 minutes, stirring occasionally. The onions should become somewhat translucent, the carrots slightly caramelized. Add salt and thyme. Dry the pig thoroughly inside and out.
You may stuff the pig with the vegetables at this time; however, if you use a conventional stuffing, such as one for a turkey, wait until just before cooking and make certain that the pig and stuffing are at room temperature. The easiest way to close the opening is to use an ice pick or an upholstery needle to punch rows of holes about an inch apart on both sides of the stomach flaps. Then lace it up with thick string just as you would a shoe. You may also use skewers and string as you would for a turkey. Because protein firms as it cooks, the pig will stay in whatever position you place it. It should resemble a dog resting on its haunches.
Place the pig in the roasting pan; it may have to be placed diagonally. Tuck the hind legs close to the stomach on either side; tie them together with string under the stomach if needed. The forelegs should be pointing straight ahead (also tied together so they won't spread out) and the head resting between them. Place a small piece of wood (like a child's block) or a piece of bunched-up foil in the mouth, opening it as wide as you can. Twist the tail into a curl and secure it with string or tape. Place crumpled aluminum foil in the eye sockets (some people place marbles). At this point you may cover it with plastic wrap and refrigerate it. Before cooking the pig, let it come to room temperature.
Preheat oven to 450°F With the oil, thoroughly baste every inch of the pig, including the head, legs and tail. Out of aluminum foil make little covers for the ears and tail. If your pig hangs over the pan, use heavy-duty foil to extend the pan so that any juices will be collected. Place the pig in the oven for 30 minutes. Remove the pig quickly, shutting the oven door, baste with oil again and return to the oven. Then reduce the temperature to 350°F Continue basting with oil every 20 minutes 4 to 5 more times (for a total of 2 hours). If the ears and tail haven't browned, remove the aluminum covers for the last 20 minutes. The total cooking time will be between 2 and 2 1/2 hours.
The cooking time is less because it is not fully stuffed; if it were, it would take an hour longer. (Approximately 10 minutes per pound lightly stuffed or unstuffed; 15 minutes per pound fully stuffed.) The pig is done when the temperature of the thigh reaches 165F (trichinae are killed when the internal temperature reaches 139F for a period of 10 minutes). When done, it may easily rest for an hour under foil or in a turned-off oven. To serve, make a garland for the pig's neck by stringing together sprigs of watercress. Make certain your apple is nicely polished. Enlist some help and very carefully slide the pig onto the platter or carving board it will be presented on. It is rather fragile at this point and can even break in half. Make a sauce by skimming the fat off the juices in the roasting pan. Place the roasting pan over 2 burners, add the stock and the wine and bring to the simmer. Stir to dissolve all the roasting juices coagulated on the bottom and continue cooking about 10 minutes. If you wish to thicken the sauce, whisk in 2 tablespoons of flour that have been blended with 2 tablespoons of butter, bring the sauce back to the boil and boil for 2 minutes, stirring. Remove any remaining foil, string or skewers. Place the apple in the pig's mouth. Place the watercress garland around its neck and bring it to the table.