Use paper towels to dry the pork shoulder. If it comes tied in butcher twine, carefully remove it.
In a small bowl, mix together the kosher salt, black pepper, garlic powder, onion powder, oregano, cumin, cinnamon, and cayenne. Rub the mixture all over the pork.
Place the pork in a 6-quart slow cooker pan with the fat cap on top. Squeeze the fresh orange juice on top. Cover and cook on LOW for 8 hours, until the meat is fall-apart tender.
Use two forks to shred the meat right in the slow cooker pan. Be careful - the pan and cooking liquids will be very hot. Mix the shredded meat well with the cooking liquids.
Preheat your oven to broil. Line a rimmed broiler-safe baking sheet with foil and spray it with oil. Remove the carnitas from the slow cooker and spread them on the baking sheet. Some of the cooking juices will remain in the slow cooker - keep it set to WARM. Spray the carnitas liberally with oil and broil them until crispy, 3-4 minutes. Keep an eye on them so that they don't burn.
Drizzle the carnitas with the remaining cooking juices. Serve immediately.
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Notes
There's no need to let the meat rest before shredding it. You actually want to shred it right away. It's true that normally it's important to allow a roast to rest before slicing it. But here, you want to shred it immediately while it's hot and very soft and mix it with the pan juices. But be careful - the pan and cooking liquids will be very hot.
The best thing about pork carnitas is the wonderful combination of soft, juicy pieces of shredded meat and crispy, caramelized pieces. To achieve this, traditionally, you would fry the cooked, shredded meat in several batches. But to make life easier, I spread the meat on a rimmed pan, spray it with oil, and broil until about half of the meat is browned and crispy.
The best cut for this recipe is pork shoulder. It's wonderfully fatty and flavorful. You could also use pork loin, but that's a much leaner cut. If you use it, the meat will not be as flavorful and will not crisp up as well. I don't recommend using pork tenderloin in this recipe. It's too lean.
You can keep the leftovers in an airtight container in the fridge for 3-4 days. Reheat them covered in the microwave at 50% power or uncovered in a 350°F oven. You can also freeze the leftovers for up to three months. This is one of those recipes where the leftovers are just as good as the freshly made dish.