Heat the butter in a large, heavy pot over medium heat. Add the onions and cook, stirring, until lightly golden, 5 to 6 minutes. Add the parsley, breadcrumbs, oysters, salt, cayenne, cheese and capers. Stir to mix and cook for 5 minutes. Remove from the heat and cool completely.
Preheat the oven to 450 degrees.
Just before roasting, fill the cavity loosely because the stuffing will expand as it cooks. Close the cavity opening with skewers and secure with kitchen twine. Tie the ends of the drumsticks together with kitchen twine. Also tie the wings back neatly under the turkey with kitchen twine.
Place the turkey on a greased rack in an uncovered roasting pan and rub well with some of the olive oil. Cover the surface of the bird (excluding the legs) with two layers of cheesecloth that have been soaked in the olive oil. Insert a roasting thermometer into the center of the thigh muscle, but don't let it hit the bone.
Put the turkey in the preheated oven and immediately reduce the heat to 350 degrees. Baste with olive oil, or pan drippings every 10 minutes during the first half hour. Baste both over and underneath the cheesecloth. Cook to an internal temperature of 180 to 185 degrees.
Remove the cloth during the last half hour of cooking to brown the bird. Carve and serve!
Note: even though the stuffing is cooked, be sure to remove all of it from the bird. Leaving it in the cavity, even refrigerated, can lead to contamination. For the same reason, make sure all the counters, cutting boards and utensils are washed in very hot soapy water.
Makes about 12 servings