Step 1: Trim any excessively large pieces of fat from the pork shoulder, but leave a good amount for flavor and moisture. Cut the pork into large, manageable chunks, about 2-3 inches thick. Place the pork chunks in a large, non-reactive bowl or a heavy-duty resealable bag.
Step 2: In a blender or food processor, combine the chipotle peppers in adobo (including a tablespoon or two of the sauce), garlic cloves, white vinegar, dried oregano, ground cumin, black pepper, and salt. Process until you have a smooth paste. Taste and adjust seasoning if necessary.
Step 3: Pour the marinade over the pork chunks, ensuring every piece is thoroughly coated. Use your hands to really work the marinade into the meat. Cover the bowl or seal the bag and refrigerate for at least 4 hours, preferably overnight, or even up to 24 hours.
Step 4: Preheat your oven to 300°F (150°C). Place the marinated pork chunks in a large Dutch oven or an oven-safe pot with a tight-fitting lid. You can add a splash of chicken broth or water (about 1/4 cup) to the bottom of the pot to prevent scorching. Cover tightly and cook for 3-4 hours, or until the pork is fork-tender. Alternatively, use a slow cooker on low for 6-8 hours or high for 3-4 hours.
Step 5: Once cooked, remove the pork from the oven or slow cooker. Transfer the pork chunks to a cutting board and let them rest for about 15-20 minutes. Reserve the cooking liquids in the pot. Using two forks or a sharp knife, thinly shave or shred the pork.
Step 6: Return the shaved pork to the Dutch oven with the reserved cooking liquid. Stir well to coat the pork in the flavorful juices. Heat gently on the stovetop over medium-low heat to ensure it’s piping hot and to slightly reduce the liquid, concentrating the flavors.
Step 7: While the pork is finishing, warm your pan árabe or pita bread. You can do this by briefly toasting them in a dry pan, on a griddle, or in a microwave until warm and pliable. Prepare your salsa Roja and any other desired toppings like thinly sliced onions or a squeeze of lime.
Step 8: Lay out a warm piece of pan árabe. Pile a generous amount of the hot, shaved pork onto the bread. Drizzle with your favorite salsa Roja, and add a sprinkle of fresh cilantro or finely diced onion if you like. Fold the bread over the filling to create a half-moon shape, or simply serve open-faced. Serve immediately.