Pat the pork shoulder dry and season it generously with paprika, cumin, chili powder, salt, and pepper. Use your hands to rub the spices all over the meat, ensuring an even coating for maximum flavor.
Heat a skillet over medium-high heat, then add a splash of oil. Sear the pork shoulder on all sides until it develops a deep golden-brown crust, about 3-4 minutes per side. This step locks in juices and adds flavor.
Place the sliced onions and minced garlic into the bottom of your slow cooker, creating a flavorful bed for the pork.
Transfer the seared pork shoulder into the slow cooker on top of the onions and garlic. Pour in the broth or water, then add the BBQ sauce and lime juice. If using, toss in a chipotle pepper or splash of apple cider vinegar for extra smoky or tangy notes.
Cover the slow cooker with its lid and cook on low for 8 hours, or until the pork is fall-apart tender and easily shreds with a fork. The house will fill with a smoky, savory aroma as it cooks.
Once cooked, carefully remove the pork from the slow cooker and transfer it to a large platter or cutting board. Use two forks to shred the meat into bite-sized pieces, watching as it falls apart into juicy strands.
Return the shredded pork to the slow cooker and stir it into the juices and sauce, allowing it to soak up the smoky, tangy flavors for about 10 minutes. This helps the meat stay moist and flavorful.
Taste the pork and adjust seasoning if needed, adding more lime juice or BBQ sauce for balance. Serve hot, with your favorite buns, sides, or garnishes.