Adjust oven rack to lowest position and heat oven to 250 degrees.
Mix brown sugar, paprika, salt, pepper, and garlic powder in a small bowl. Pat roast dry and place on a rack set over a foil lined shallow baking sheet. Lightly sprinkle top and sides of roast with salt, brush with half the mustard, and sprinkle with half the spice rub. Carefully turn roast over. Sprinkle with a little salt, brush with remaining mustard, and sprinkle with remaining spice rub.
Roast until a meat thermometer registers 170º, 9 to 11 hours, depending on the size. Transfer pork to a platter and let cool enough to handle, about 1 hour.
Meanwhile, if making sandwiches and pork needs a little more moisture, pour off any fat and scrape pan drippings into a small saucepan, add 1 cup water and bring to a simmer. Remove from heat.
Cut roast into 1 to 2-inch chunks and shred meat into a large bowl. Add enough pan drippings to moisten pork and stir to combine.
Serves 12 to 20.