Preheat your oven to 300°F (150°C). In a small bowl, mix smoked paprika, brown sugar, chili powder, garlic powder, onion powder, cumin, salt, and pepper to create a dry rub. Rub the pork shoulder with olive oil, then massage the dry rub all over the meat, ensuring it's well-coated.
Place the pork in a roasting pan and add chicken broth or apple juice to the bottom of the pan. Cover the pan tightly with foil and roast in the preheated oven for about 4-6 hours or until the pork easily shreds with a fork.
In a saucepan over medium heat, combine ketchup, brown sugar, apple cider vinegar, Dijon mustard, Worcestershire sauce, smoked paprika, salt, and pepper. Stir well and bring the mixture to a simmer. Reduce the heat and let it simmer for 15-20 minutes, stirring occasionally, until the sauce thickens.
Once the pork is fork-tender, remove it from the oven. Use two forks to shred the meat directly in the roasting pan, incorporating the cooking juices for added flavor.
Pour the prepared BBQ sauce over the shredded pork and mix thoroughly to coat the meat evenly.
Slice the slider buns in half and lightly toast them. Spoon a generous portion of the pulled pork onto the bottom half of each slider bun. Top with coleslaw if desired, and place the other half of the bun on top.
Serve the pulled pork sliders warm, accompanied by pickles on the side for a tangy crunch.