To make the rub, combine the butter with the rest of the ingredients, and mash all together to make a paste.
To prepare the pork, rinse the pork shoulder under cold running water and pat it dry with paper towels. With a large sharp knife, stab the pork all over the surface, including the top, bottom, and sides, penetrating about 2 inches into the flesh. Using your hands, rub the paste all over the pork shoulder, working the mixture into the slits and under the skin. Lard the pork with the olives and garlic in the slits. Place the pork, skin side up, in a large roasting pan, cover with plastic wrap, and let marinate in the refrigerator for a minimum of 3 hours or up to 2 days.
When you're ready to roast the pork shoulder, adjust an oven rack to the lowest position, removing other racks if needed. Preheat the oven to 400 degrees.
Remove the pork from the refrigerator and let it sit for 30 minutes to bring it to room temperature. Pour enough chicken stock or water into the pan to come about 1 inch up the sides of the pork. Cover the pan tightly with foil and braise the pork for 3 hours, or until the meat is tender. Take the pork from the oven. Remove and discard the foil, and return it to the oven to roast, uncovered, for 1 hour, or until the skin is dark brown and crisp. Set the pork aside to rest for 10 minutes before serving. Slice and serve.