The Smokehouse Stackup

Prepare the dry rub by combining the smoked paprika, dark brown sugar, garlic powder, onion powder, salt, black pepper, and cayenne pepper in a small bowl. Stir until evenly blended.

Pat the pork shoulder completely dry with paper towels. Rub the spice mixture generously over all surfaces of the meat, pressing it into the crevices. Let the seasoned pork sit at room temperature for 15 minutes while you preheat the oven.

Preheat the oven to 300 degrees Fahrenheit with a rack in the lower third position.

Heat the vegetable oil in a large Dutch oven over medium-high heat until the oil shimmers and just begins to smoke. Sear the pork shoulder for 3 to 4 minutes per side, turning with tongs, until a deep brown crust forms on all major surfaces. This should take about 12 minutes total. Do not skip this step, as the sear builds the foundation of flavor.

Remove the Dutch oven from the heat. Pour the apple cider vinegar and chicken broth around the sides of the pork (not directly over the top, which would wash off the spice crust). The liquid should come about one-third of the way up the side of the meat.

Cover the Dutch oven with its lid and transfer to the oven. Braise for 3.5 to 4 hours, until the pork is completely tender and falls apart easily when prodded with a fork. The internal temperature should read at least 200 degrees Fahrenheit.

While the pork braises, prepare the slaw. Toss the shredded cabbage and grated carrot together in a medium bowl. In a small bowl, whisk together the mayonnaise, 1 tablespoon of apple cider vinegar, sugar, and a pinch of salt. Pour the dressing over the cabbage mixture and toss until evenly coated. Cover and refrigerate for at least 1 hour so the flavors meld and the cabbage softens slightly.

When the pork is done, transfer it to a large cutting board or rimmed sheet pan. Pour the braising liquid from the Dutch oven through a fine-mesh strainer into a fat separator or measuring cup. Let it sit for a few minutes, then skim or separate the fat.

Using two forks, shred the pork into bite-sized strands, discarding any large pieces of fat or connective tissue. Transfer the shredded pork back to the Dutch oven.

Add the barbecue sauce and about 1/2 cup of the defatted braising liquid to the shredded pork. Stir everything together over medium-low heat for 3 to 4 minutes until the pork is glossy, saucy, and heated through. Add more braising liquid if you prefer a looser, juicier consistency.

Split the brioche buns and toast them cut-side down in a dry skillet over medium heat for about 60 seconds, or until golden brown on the cut surfaces.

Pile a generous mound of saucy pulled pork onto each toasted bun bottom. Top with a handful of the chilled vinegar slaw, letting it spill over slightly. Press the bun top on gently and serve immediately with extra barbecue sauce and pickles on the side.