Prepare the Pork: Mix cumin, smoked paprika, oregano, brown sugar, salt, and pepper in a bowl. Rub the mixture all over the pork shoulder.
Sear the Pork: Heat oil in a skillet over medium-high heat. Sear the pork on all sides until browned.
Slow Cook: Transfer the pork to a slow cooker. Add onion, garlic, chipotle peppers, adobo sauce, and chicken broth. Cook on low for 8-10 hours or on high for 5-6 hours.
Shred and Serve: Remove the pork, shred it, and return it to the sauce. Stir in lime juice and serve.