1) Rinse the pork shoulder and place in a large container, pour in the brine solution until the shoulder is completely covered. Cover the container and place in the refrigerator for at least 8 hours.
2) Remove pork shoulder from brine solution, pat dry with paper towels, place in baking pan that is bigger than the shoulder by at least a inch in length and width and at least 3 inches deep. Sprinkle dry rub onto the surface of the shoulder and massage in such that it adheres to the surface. Coat all sides. Make sure the fat layer on the shoulder is facing up before cooking! Place baking pan uncovered in a 225 degree F oven on the middle rack. Insert a probe thermometer into the center or thickest part of the shoulder, but not touching the bone. Monitor the temperature throughout cooking (a digital thermometer with an alarm function is the easiest way to do this). Do not remove from the oven until the center of the shoulder reaches 200 degrees.
3) When the shoulder has reached 200 degrees, shut off the oven and let the roast cool for a couple of hours before removing from the oven. If the bottom of the pan is dry (or crusted with dried spices) then cover the pan with foil to retain internal moisture of the meat during the cooling period. When the temperature drops to 170 degrees or slightly lower, remove from oven. Place on a large, clean work surface such as a cutting board, and remove the large sheet of crusted fat on the top. Pull apart with two forks, it will pull apart very easily. Serve for friends and family!