Preheat oven to 300ºF.
In a small bowl, mix all spices and brown sugar. Rub mixture all over pork shoulder.
Heat olive oil in a Dutch oven over medium-high. Sear pork on all sides until browned (about 7–9 minutes total).
Add chicken broth, scraping any browned bits. Bring to a simmer, cover, and transfer to oven.
Bake for 3 hours covered, then uncover and bake 1 hour more, until pork is fall-apart tender. Add more broth as needed to keep it moist.
Shred pork with two forks. Set aside and keep warm.
Preheat oven to 350ºF. Line a baking sheet with parchment or foil.
Slice rolls horizontally, keeping them connected. Place bottom half on baking sheet.
Spread yellow mustard on the bottom half of the rolls.
Layer the fillings: Lay down ham slices (1 per slider), evenly distribute roast pork (about ¼ cup per slider), top with Swiss cheese halves, and add 2 pickle chips per slider.
Replace the top half of the rolls.
Brush melted butter over tops of rolls. Sprinkle with poppy seeds if using. Press down to flatten the sliders a little.
Bake for 8-10 minutes until melted and toasted.
Slice, serve, and watch them vanish.
