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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.
Heat a cast iron skillet over medium-high. Add ham slices and sear until browned, about 1–2 minutes per side.
Drizzle honey over the slices in the last 30 seconds of cooking to caramelize. Remove from heat. Lower heat to medium on the cast iron skillet.
Slice bread into 2 portions and cut each in half lengthwise.
On the same cast iron skillet, add 1 tbsp butter and place the bottom slice of 1 bread and start topping with the following: Layer in this order: Yellow mustard, Swiss cheese, Honey Ham, Roasted Pork, Pickles, Pickled jalapeños, Another layer of Swiss cheese.
Close sandwich and spread butter on the outside of the bread. Press down and flip. Continue to press down to flatten sandwich and grill on both sides. Lower heat if starting to burn.