1/2 cup plus 1/2 teaspoon kosher salt, divided
1/2 cup sugar
1 boneless pork shoulder butt roast (about 3 pounds)
1/2 cup water
1/2 cup barbecue sauce
1/3 cup gochujang (Korean red pepper paste)
1/4 cup packed brown sugar
3 tablespoons cider vinegar
1/2 cup mayonnaise
2 tablespoons minced fresh cilantro
2 tablespoons lime juice
12 brioche hamburger buns, split and toasted
Chopped lettuce, bread and butter pickle slices, thinly sliced jalapeno pepper and fresh cilantro leaves
Combine 1/2 cup salt and sugar; rub onto all sides of roast. Wrap pork in foil; place in a shallow dish. Refrigerate overnight.
Unwrap pork. Using a kitchen knife, scrape salt and sugar coating from roast; discard any accumulated juices. Transfer pork to a 6-qt. electric pressure cooker; add water. Lock lid; close pressure-release valve. Adjust to pressure-cook on high for 60 minutes. Let pressure release naturally for 15 minutes; quick-release any remaining pressure.
Remove roast to a cutting board; let rest 15 minutes. Pour cooking liquid into a glass measuring cup and let fat rise to surface. Skim fat; discard. Reserve 1/2 cup cooking liquid; discard remaining cooking liquid. When cool enough to handle, shred meat with 2 forks. Place shredded meat in a foil-lined rimmed baking pan.
Preheat broiler. In a small bowl, combine barbecue sauce and gochujang. Stir in brown sugar, vinegar and reserved cooking juices. Pour over pork; toss to coat.
Broil 3-4 in. from heat until pork is crispy, 12-15 minutes, stirring occasionally. Combine mayonnaise, cilantro, lime juice and remaining 1/2 teaspoon salt; spread over cut sides of buns. Place pork mixture on bun bottoms. Top with lettuce, pickles, jalapeno and cilantro; replace bun tops.