Mix all the marinade ingredients together in a large bowl.
Reserve 1 cup of the marinade for later.
Place the pork shoulder in the marinade, coating the entire pork shoulder in marinade.
Cover and allow to marinade for minimum 2 hours or up to 8 hours in the fridge.
Remove the pork from the fridge.
Preheat the smoker to 250℉.
Add wood chips to the smoker, or pellets, depending on your smoker.
When the smoker is ready, add the pork shoulder to the smoker.
Close the lid and allow to smoke/cook until pork reaches an internal temperature of 201-205℉
Remove from smoker and wrap in foil to rest 1 hour.
Place pork in a large roasting pan and shred the meat using forks.
Once shredded, add the reserved marinade to the pork, mixing to combine.
Slice the slider buns.
Top the bottom halves of the slider buns with 6 slices of cheese, then 6 slices of ham.
Top the ham with pulled pork, pickles, and 6 slices of mozzarella cheese.
Spread mustard on the top buns.
Place top buns on top of the sliders.
Brush with melted butter and sprinkle with sesame seeds or poppy seeds.
Place the sliders on a tray and heat in the smoker or on a BBQ until the cheese is melted and the tops of buns are golden.
Serve hot.