Prepare the pulled pork. Place the pork shoulder in a large bowl. Combine sugar, chili powder, paprika, garlic powder, salt, black pepper, and onion powder. Rub the mixture all over the pork. Place the onions under the pork. Cover and refrigerate for 8 hours or overnight.
Preheat the oven to 300°F. Place pork shoulder in a large cast iron Dutch oven or roasting pan. Cover the roast with aluminum foil. Roast for 5 hours. Increase oven temperature to 375°F and uncover the roast. Cook for 1 more hour, basting the pork with the juices. Remove from oven and allow the roast to rest for 30 minutes. Shred the pork.
Prepare the barbecue sauce. In a medium saucepan, melt butter over medium heat. Add onion, garlic, and salt. Sautee until onion is tender. Stir in paprika, chili powder, dry mustard, black pepper, water, vinegar, and sugar. Bring mixture to a simmer. Add ketchup and stir until incorporated.
Bring mixture to a simmer and cook, uncovered, for 20-25 minutes or until thickened. Stir occasionally. Remove the mixture from the heat. Using an immersion blender, blend mixture until smooth. If you do not have an immersion blender, transfer sauce to a blender and blend until smooth.
Prepare the sliders. Add pulled pork, sauce, and coleslaw to the slider buns and enjoy!