Place the pork shoulder on a cutting board or baking sheet. Whisk together the brown sugar, ginger, paprika, black pepper, salt and garlic in a small bowl. Rub the spice mixture all over the pork butt.
Pour the beer and orange juice into a large Dutch oven and add the pork. Cook, uncovered, basting with any juices that accumulate in the pan, until the pork reaches an internal temperature of 200 degrees F and shreds easily, 6 to 7 hours. Let the pork rest for 10 to 15 minutes, then shred. Serve on brioche buns.