Pat the pork shoulder dry with paper towels. In a small bowl combine brown sugar, smoked paprika, ground cumin, dried oregano, kosher salt, and black pepper. Rub the vegetable oil over the pork, then massage the dry spice mix all over the meat, pressing into any crevices.

Sear

Heat a large heavy oven-safe Dutch oven or large skillet over medium-high heat. Add 1 tablespoon oil if needed. Sear the pork on all sides until deeply browned, about 3–4 minutes per side. Transfer pork to a plate.

Braise

Reduce heat to medium. Add orange juice, lime juice, minced garlic, apple cider vinegar, and chicken/pork stock to the pot, scraping up brown bits. Return the pork to the pot, cover tightly with a lid. Bring to a gentle simmer, then transfer to a preheated oven at 300°F (150°C). Roast for 3 to 3.5 hours, or until the pork is fork-tender and pulls apart easily. Check after 2 hours and add up to 1/2 cup water or stock if the liquid is evaporating too quickly.

Shred and finish

Carefully remove pork to a cutting board and let rest 10 minutes. Strain and reserve braising liquid. Using two forks, shred the pork into bite-sized pieces. Skim fat from the reserved liquid and discard excess fat. Mix 1 cup of BBQ sauce with 1/2 cup reserved braising liquid and return to the shredded pork in the pot over low heat to warm and coat. Taste and adjust seasoning with salt and pepper if needed. Keep warm until assembly.

Chipotle Slaw

Make dressing

In a medium bowl combine mayonnaise, Greek yogurt, minced chipotle, adobo sauce, lime juice, honey, salt, and black pepper. Whisk until smooth and well blended.

Toss slaw

Place shredded green cabbage, red cabbage, and grated carrot in a large bowl. Pour the dressing over the vegetables and toss until evenly coated. Taste and adjust seasoning (add more adobo or chipotle for heat, more lime for brightness). Refrigerate at least 20 minutes to let flavors meld; can be made up to 24 hours ahead and drained slightly before using if very wet.

Pickles & Plantains

Prepare plantains

Peel the ripe plantains and slice on the diagonal into 1/4-inch thick pieces. Pat slices dry with paper towels. Heat 1 cup vegetable oil in a medium skillet over medium-high heat until shimmering (about 350°F/175°C if using a thermometer).

Fry plantains

Fry plantain slices in batches, avoiding overcrowding, until golden brown and caramelized, about 2 minutes per side. Transfer to a paper towel-lined plate and immediately sprinkle with salt and, if desired, a pinch of brown sugar for extra sweetness. Keep warm in a low oven (200°F/95°C) while finishing other batches.

Pickles ready

Drain pickle slices on paper towels if needed. No additional prep required; keep covered in refrigerator until assembly.

To Assemble

Toast buns

Butter the cut sides of the buns lightly. Toast in a hot dry skillet or under a broiler until golden, about 1–2 minutes per side. Keep warm.

Build sandwiches

Place a generous helping (about 1/2 cup) of warm pulled pork on the bottom bun. Spoon an additional 1–2 tablespoons of the warmed BBQ-braising sauce over the pork if desired. Top pork with a heaping 1/3 cup of chipotle slaw, arrange 2 pickle slices, and add 2–3 fried plantain slices. Garnish with a few cilantro leaves if using. Close with top bun.

Serve

Serve immediately with extra BBQ sauce on the side. Leftover pork can be refrigerated for up to 3 days or frozen for up to 3 months.