Remove the pork shoulder from the brine solution, pat dry with paper towels, and place in a baking pan that is bigger than the shoulder by at least a inch in length and width and at least 3 inches deep.
Sprinkle the dry rub onto the surface of the shoulder and massage it in so that it adheres to the surface, coating all sides. Make sure the fat layer on the shoulder is facing up before cooking!
Place the 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.
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 has dropped 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!