Cut pork into 3 or 4-inch cubes, trimming away any thick fat (I was left with 3 1/2 pounds after trimming). Sprinkle lightly with salt on all sides.
Juice the orange, saving halves. Discard any seeds, reserve 1/3 cup juice.
In a large Dutch oven or heavy-bottom saucepan, melt the lard over medium-low heat. Once it’s melted, add the pork, orange juice, orange halves, water, onion, garlic, and cinnamon stick. The liquid and fat should cover the pork completely. If it doesn’t, add a bit more water or leftover orange juice.
Gently simmer, stirring occasionally, until the meat is tender, around 2 hours. If the water evaporates during the cooking process, add more as needed to keep the pork submerged (don't add too much; you want the liquid to be evaporated by the end).
Once the meat is tender, turn the heat up to medium-high and evaporate any remaining water. You'll know the water has evaporated when the bubbles become smaller, meaning only the lard is simmering.
Cook for an additional 10-30 minutes (mine took 10), stirring occasionally, until the meat is caramelized and crispy. If the bottom of the pot develops a brown glaze at any point that looks like it might burn, deglaze with a couple tablespoons of water, scraping up the brown bits and stirring them into the meat.
Line a cutting board or large plate with paper towels. Using kitchen tongs or a slotted spoon, transfer the meat to drain on the paper towels. Once the meat is cool enough to handle, shred with two forks or clean fingers (I found it easier to do with my hands since the exterior is firm). Add more salt to taste if needed (I added 1/2 teaspoon).
Serve in warm corn tortillas with toppings of your choice. Store leftovers in an airtight container in the refrigerator for up to 4 days. You can also freeze the leftovers; use within 3 months.
I purchased lard on Amazon. It’s what I recommend using in this recipe for best results, but you can substitute clarified butter or ghee. Another option is to use a high heat, neutral oil (such as vegetable oil), but it won't be quite as tasty.I recommend saving some of the leftover lard from the pot to use when reheating the meat. You can reheat in the microwave or a saucepan; top with a small dollop of fat, just enough to lightly coat the meat once melted. Don’t throw the remaining lard down your sink or it will clog the pipes. Toss it in the trash.Recipe is my own, technique is adapted from Emeril.