Step 1: Prepare the Pork : Pat the pork shoulder dry with paper towels. In a small bowl, combine paprika, chili powder, cumin, brown sugar, salt, and pepper. Rub the spice mixture evenly over the pork.
Step 2: Sear the Pork (Optional but Recommended) : Heat olive oil in a large skillet over medium-high heat. Add the pork and sear on all sides until browned (about 3–4 minutes per side). This step locks in flavor and adds a smoky crust.
Step 3: Slow Cook the Pork : Place the onion slices and garlic at the bottom of a slow cooker. Set the seared pork on top. Pour in barbecue sauce, chicken broth, vinegar, and Worcestershire sauce. Cover and cook on LOW for 8 hours or HIGH for 4–5 hours, until the pork is fork-tender and easily shredded. (Oven method: Place everything in a Dutch oven, cover with foil or lid, and bake at 325°F / 165°C for 3–4 hours.)
Step 4: Shred the Pork : Remove the pork from the cooker and shred it using two forks. Discard any large chunks of fat. Return shredded pork to the slow cooker and mix with the cooking juices. Let it soak on WARM for 15–20 minutes.
Step 5: Make the Coleslaw : In a large bowl, whisk together mayonnaise, vinegar, honey, salt, pepper, and celery seeds. Add the cabbage and carrots, and toss until evenly coated. Chill for 30 minutes before serving.
Step 6: Assemble the Sandwich : Toast the buns lightly for extra crunch. Pile a generous portion of pulled pork on the bottom bun. Add a drizzle of barbecue sauce. Top with a scoop of coleslaw and close with the top bun. Serve immediately and enjoy the juicy, smoky perfection!