Prepare the Pork: Leave most of the fat cap intact, removing only large hard pieces. Cut the pork into large 3 to 4-inch chunks and pat lightly dry with paper towels.
Season the Pork: Place pork into a large bowl or pan. Add kosher salt, black pepper, cumin, Mexican oregano, 4 smashed garlic cloves, and 1 tablespoon lard. Massage the seasonings thoroughly into every piece of pork.
Marinate for Flavor: Cover tightly and refrigerate for 24 hours to deeply season the meat and help retain moisture. Do not add the onions, citrus, or Coca-Cola at this stage.
Bring to Room Temperature: Remove the pork from the refrigerator about 45 minutes before cooking to promote even cooking.
Prepare Aromatics: Cut the onion into large chunks and smash the remaining 2 garlic cloves. No need to mince.
Prepare Citrus: Quarter the orange and halve the lime. Leave the peels on to add flavor during cooking.
Build the Cooking Pan: Place the seasoned pork into a roasting pan, Dutch oven, or deep foil pan. Add onion chunks, smashed garlic, orange pieces, lime pieces, bay leaves, and cinnamon stick. Pour in the Mexican Coca-Cola and add the remaining tablespoon of lard.
Slow Roast: Cover tightly with a lid or heavy-duty foil. Bake at 300°F until the pork is fork tender and nearly collapses when touched, about 5 to 6 hours.
Remove Aromatics: Discard bones, bay leaves, citrus peels, and cinnamon stick. Leave the softened onions and garlic in the pan for extra flavor.
Reserve the Liquid: Carefully collect the cooking juices and rendered fat from the bottom of the pan. Set aside for finishing and holding.
Shred the Pork: Using forks or gloved hands, shred the pork into medium rustic pieces. Avoid shredding too finely to maintain texture and juicy bites.
Adjust Seasoning & Serve: Taste and add additional salt or fresh lime juice if needed. The pork should taste slightly bold since tortillas, rice, and toppings will mellow the flavor.