Prepare the ingredients by dicing the onion and mincing the garlic. Rinse and chop green chilies and tomatillos if using fresh.

In a large pot, heat a tablespoon of oil over medium-high heat. Sear the pork shoulder for 4-5 minutes on each side until golden-brown.

Remove the seared pork and add diced onion and minced garlic to the pot, sauté for 3-4 minutes until translucent.

Stir in the chopped green chilies and tomatillos, along with cumin, oregano, salt, and freshly cracked pepper. Cook for 5-7 minutes.

Return the pork shoulder to the pot and add enough water or broth to cover the meat halfway. Simmer on low for 2-3 hours.

Once the pork is tender, shred it using two forks and return it to the pot. Simmer for an additional 10-15 minutes.

Serve hot, garnished with chopped cilantro and lime wedges.

If there are leftovers, let them cool and store in airtight containers for freezing.