Prepare the spice rub by combining packed light brown sugar, salt, smoked paprila, garlic powder, onion powder, ground cumin, cayenne pepper, and ground black pepper. Mix the spices until well combined.
Cut the pork butt into 4 to 6 equal pieces. Then season with the spice rub, making sure to press the spices into the pork until well coated.
Set the Instant Pot to 'saute' mode. Once heated, add neutral oil then sear the pork on all sides until browned, about 1 minute per side. If making this in a slow cooker, sear the pork in a pot then transfer to the slow cooker. If making this in the oven, preheat to 300F (150C). Sear the pork in a heavy duty oven-safe pot.
Pour in the Pepsi then cover with the lid. Cook on high pressure for 1 hour, making sure the vent is set to sealing. After 1 hour, allow for natural release, which should take about 20 minutes. For the slow cooker method, cook on low for 8 hours. For the oven, cover with lid and bake for 4 hours, or until fork tender.
While the pork is cooking, prepare the BBQ sauce by mixing ketchup, Dijon mustard, apple cider vinegar, soy sauce, light brown sugar, honey, Worcestershire sauce, paprika, and cayenne pepper. You can also use pre-made bottled BBQ sauce, about 3/4 cup or to taste.
Remove the pork from the Instant Pot and set aside to cool. When the pork is cool to the touch, shred it with your hands or two forks. Ladle 1/4 cup of the juices from the Instant Pot over the shredded pork. Add the BBQ sauce and mix well.
Preheat the oven to 350F (175C).
Slice the slider buns in half, making sure not to tear apart each individual slider. Remove the top half of the slider buns then arrange the pulled pork on the bottom half. Add a generous layer of shredded mozzarella cheese then place the top half of the slider buns on top.
In a small bowl, mix melted butter, minced garlic, and chopped fresh parsley. Brush the top of the slider buns with the garlic butter.
Transfer to the oven in the middle rack. Bake for 5 to 10 minutes, until the cheese has melted.
Serve and enjoy!