Heat olive oil in a large pot over medium-high heat.
Sear the pork shoulder on all sides until browned.
Remove the pork from the pot and set aside.
Add chopped onion to the pot and sauté for about 5 minutes until translucent.
Stir in minced garlic and cook for an additional minute.
Return the pork to the pot and add chicken broth, apple cider vinegar, brown sugar, smoked paprika, cumin, salt, and pepper.
Bring the mixture to a simmer, then cover and reduce heat to low.
Cook for 6-8 hours, or until the pork is tender and easily shreds.
Remove the pork and shred it using two forks.
Return the shredded meat to the pot and stir to combine with the sauce.