Pulled pork: preheat your oven to 350 degrees F (175 C).
Wipe down and dry your pork shoulder or pork butt. And your regular butt if needed. Wash your hands.
In a small bowl add your salt, smoked paprika, and black pepper. Mix well. This is your rub.
Cover and rub your pork fully with all your rub. Make sure no parts of the pork are unseasoned.
In a dutch oven or large oven-safe pot, add your fully seasoned pork and place it in the middle.
Pour 1 cup of apple cider vinegar into the dutch oven or pot, around the pork.
Add a lid or cover to your oven-safe pot and add it to the preheated oven.
Cook for 3 hours with the cover on the pot. If you don't have a cover, you can cover the pot with aluminum foil.
Once 3 hours are over, remove the cover/lid for the pot and cook for an additional 30 minutes.
Remove pork from the pot (don't discard any liquid left in the pot just yet), place it on a cutting board and allow the meat to rest for 45 minutes to 1 hour then pull meat from the bone and use two forks to separate it. If you really want the Eastern North Carolina experience, take your sharpest chef knife or cleaver, and finely chop the pulled pork.
After you pull the pork and/or chop it, add all of the meat to a container that you can store in your refrigerator (unless you plan to eat it all in one sitting). If there was any liquid left in the pot you cooked the pork in, you can pour that into the container with all of the meat.
Parmesan cilantro compound butter: combine all compound butter ingredients in a small bowl and using a spoon, mash it all around to combine.
Store in a sealed container or wrapped in plastic wrap in your refrigerator for up to 2 weeks.
Sandwich assembly: warm up the pulled pork for 5 or 6 minutes in a skillet or griddle over medium heat. The pork should crisp up a little in places, which will add texture to the final sandwich.
While the pork is crisping up, spread 2 to 3 tablespoons of the compound butter on just 1 side of each slice of sourdough bread.
Remove the pork after it is crispy and hot and place it in a bowl for just a few minutes. Wipe out the pan.
Place both slices of your bread, compound butter side down, on the pan or griddle over medium-low heat.
Add condiments, mayonnaise, or mustard to the two exposed slices of bread in the pan.
Add slices of cheese on top of the condiments - cover with a metal bowl or lid of the pan for 1 minute to help melt the cheese
Add the warm, crispy pork on top of the cheese. Top the pork with slices of pickled jalapenos. Close the sandwich by putting the second slice of bread on top of the jalapenos, cheese side down.
pay attention to the color on the top of the sandwich this is what color the bottom bread is, try not to let it get too dark,
flip occasionally until the color looks toasted enough for you.
Allow sandwich to cool for 1 to 2 minutes on a cooling rack and serve.