In a small bowl, combine brown sugar, salt, black pepper, paprika and garlic powder. Rub the pork on all sides with this mixture.
Add 1-2 tablespoons of oil to a cast iron skillet (or other nonstick skillet) over high heat. Once the skillet is very hot, carefully add the pork and sear on each side for about 30 seconds until a nice crust forms.
Transfer pork roast to a crockpot along with apple cider vinegar and water. Cook on high heat for 4 hours or on low heat for 8 hours. When done, pork will be very tender and pull apart easily with a fork.
While the pork is cooking: Make garlic aioli by whisking ingredients together in a small bowl. Cover and place in the fridge until ready to use.
About 15 minutes before you are ready to eat, make the balsamic glaze. Add balsamic vinegar, and brown sugar to a saucepan. Cook over medium heat until sauce thickens and turns into a glaze, stirring occasionally, about 10-15 minutes.
Remove pork from the crockpot and toss with the balsamic glaze.
Heat a large skillet to medium-high heat with a little butter. Place buns cut side down on skillet and toast until golden. Or you can just toast them in a toaster oven.
Spread garlic aioli on each bun and pile balsamic pork on each bun. Serve sandwiches with your favorite side dishes! Enjoy!!