Pulled pork and onions: pre-heat your oven to 350 degrees F (175 C).
In a small bowl add brown sugar, salt, 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.
Slice both ends off of 4 Vidalia onions. Cut them in half and peel.
In a dutch oven or large oven-safe pot, add all your onion halves, cut side down. Add the fully rubbed pork and place it in the middle of the pan on top of the onions.
Add a lid or cover to your oven-safe pot and add it to the preheated oven. You can cover the pot with aluminum foil if you don't have a cover.
Cook for 3 and a half hours with the lid on the pot.
Once 3.5 hours are over, remove the cover/lid for the pot and cook for an additional 30 minutes.
Remove the pork from the pot, place it on a cutting board, and allow the meat to rest for 45 minutes to 1 hour. Remove the onions from the liquid with a strainer. Move the onions to their own container or the container where you plan to put the pulled pork.
After the meat has rested, pull meat from the bone and use two forks to separate it. At this point, you can mix in the onions or keep them in separate containers.
Japanese-style barbecue sauce: in a medium-sized bowl add all the ingredients for this sauce. Stir well to incorporate.
Store in a sealed container in your refrigerator.
Sandwich assembly: toast your bun if desired.
In a small to medium pan over medium heat, add a bun-sized amount of your pulled pork and a few of the cooked onions. Cook until everything is warm, about 5 minutes.
After 5 minutes, remove the pan from the heat and toss the pork in a few tablespoons of your Japanese-style barbecue sauce.
Add the sauced pork to the bottom bun and then top with onions or mix the onions in with the pork.
Add the sliced cheese to the top of the meat and onions and place under the oven broiler on high for 3 or 4 minutes or until the cheese is melty.
Top with a few slices of pickled jalapenos and then finish the sandwich with the top bun.