For the BBQ pork: Whisk together the smoked paprika, salt, garlic powder and onion powder in a large bowl. Add the pork shoulder and turn to coat.
Heat the oil in a large saute pan over low heat and cook the pork, turning occasionally, until all sides are golden, 8 to 10 minutes.
Remove the pork to a plate. Combine the onions with the chili sauce, vinegar, brown sugar and 1 cup water in a slow cooker and whisk together. Add the pork shoulder, cover and cook on low until the pork is hot and cooked through, 8 to 10 hours.
Remove the pork to a cutting board and set aside. Pour the liquid into a medium saucepan. Bring to a boil and cook over high heat until reduced by half or the sauce is thick, 8 to 10 minutes.
Meanwhile, shred the pork with 2 forks or chop into pieces. Put back in the slow cooker and top with the reduced sauce, to taste.
For the slaw: Whisk together the mayonnaise, mustard, vinegar, sugar, salt and pepper in a large bowl. Add the cabbage and carrots and toss until coated.
To serve, place the pulled pork on the bottom buns, top with the slaw, then close the sliders.