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In a small bowl, mix together the smoked paprika, chili powder, cumin, salt, pepper, oregano, and brown sugar to make a dry rub.
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Pat the pork shoulder dry with paper towels and coat it evenly with the spice mixture, pressing it into the meat.
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Heat olive oil in a large skillet over medium-high heat. Sear the pork on all sides for 2–3 minutes per side, until browned.
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Place the sliced onion and minced garlic in the bottom of your slow cooker. Set the seared pork shoulder on top.
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Pour in the chicken broth, apple cider vinegar, and soy sauce (or Worcestershire sauce).
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Cover and cook on low for 8–10 hours or on high for 5–6 hours, until the pork is very tender and easily shreds with a fork.
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Remove the pork from the slow cooker and shred it using two forks. Skim off excess fat from the cooking liquid, then return the shredded meat to the pot and mix with the juices.
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Serve warm with fresh herbs, over rice, in tacos, or with your favorite barbecue sauce.