Preheat the oven to 325°F.
Pat the 5-pound bone-in pork shoulder completely dry with paper towels. In a small bowl, combine 2 teaspoons smoked paprika, 2 teaspoons cumin, 1 teaspoon dried oregano, 1 teaspoon garlic powder, 2 teaspoons kosher salt, and 1 teaspoon black pepper. Rub the seasoning mixture over every surface of the pork. Let the pork rest at room temperature for 30 minutes.
Heat 1 tablespoon olive oil in a large Dutch oven over medium-high heat. Sear the pork for 4 to 5 minutes per side, until deeply browned all over.
Transfer the pork to a plate. Add the roughly chopped yellow onion to the pot and cook for 3 minutes, scraping up any browned bits from the bottom. Stir in the 6 smashed garlic cloves and cook for 1 minute, until fragrant.
Add the 4 chipotle peppers, 2 tablespoons adobo sauce, 1 cup freshly squeezed orange juice, 1 cup chicken broth, and 2 tablespoons brown sugar. Stir everything together until combined.
Nestle the pork back into the Dutch oven, fat side up. Cover with the lid and transfer to the oven. Braise for 3½ to 4 hours.
Start checking the pork after 3½ hours. It’s ready when it shreds effortlessly with two forks. If it still feels firm or stringy, cover and continue braising, checking every 20 to 30 minutes until it’s fall-apart tender.
Transfer the pork to a cutting board. Remove and discard the bone and any large pieces of fat, then shred the meat with two forks or an automatic shredder.
Return the shredded pork to the Dutch oven and stir it into the braising liquid. Taste and season with additional salt if needed.