In a small bowl combine kosher salt, black pepper, brown sugar, paprika, garlic powder, onion powder, ground cumin and cayenne pepper. Mix thoroughly so sugar and spices are evenly distributed.

Trim and coat pork

Pat the pork shoulder dry with paper towels. Trim any excessively thick hard fat, leaving a thin fat cap to keep meat moist. Rub the yellow mustard all over the pork to help the dry rub adhere, then coat it evenly with the prepared dry rub, pressing it into the meat on all sides.

Sear (optional, for flavor)

Heat olive oil in a large heavy-bottomed Dutch oven or skillet over medium-high heat until shimmering. Sear the pork shoulder on all sides, 3–4 minutes per side, until browned. This step is optional but adds depth of flavor.

Add aromatics and liquids

Place the quartered onion and smashed garlic cloves in the bottom of a slow cooker or Dutch oven. Put the seared (or unseared) pork on top. Pour in the apple cider vinegar and stock around the pork (not over the rub), and add liquid smoke if using. The liquid should come up about 1–1.5 inches but not cover the pork.

Slow-cook until tender

Slow cooker method: Cover and cook on LOW for 8–9 hours or HIGH for 5–6 hours, until the pork is fall-apart tender and an internal temperature of at least 195–205°F (90–96°C) is reached. Oven method: Preheat oven to 300°F (150°C). Cover the Dutch oven and roast for 4.5–6 hours, checking after 4 hours, until pull-apart tender. For faster stovetop/instant pot: Use pressure cook on high for 60–75 minutes (depending on size) with natural pressure release for 15 minutes.

Rest and shred

Carefully remove the pork to a large cutting board or roasting pan and reserve the cooking liquid. Let the pork rest 15–20 minutes to allow juices to redistribute. Using two forks or meat claws, shred the pork into bite-sized pieces, removing any large pieces of fat or bone. Toss shredded meat with some reserved cooking liquid (a few tablespoons at a time) to keep it moist.

Finish with barbecue sauce

Transfer shredded pork to a bowl or back into the warm pot. Add the barbecue sauce and toss gently until evenly coated. Taste and adjust seasoning with additional salt, pepper, or a splash of apple cider vinegar for brightness. Keep warm until serving.

To Serve

If serving on buns, lightly toast buns on a pan or under broiler. Pile warm pulled pork onto buns, top with prepared coleslaw and pickles as desired. Alternatively serve plated with extra barbecue sauce and a side of coleslaw.