Trim excess fat from the pork shoulder, leaving a thin layer for flavor. Pat the meat dry and rub with smoked paprika, brown sugar, salt, and black pepper, massaging seasonings into all sides.

Sear

Heat vegetable oil in a large Dutch oven or heavy oven-safe pot over medium-high heat. When hot, sear the pork on all sides until browned (about 3–4 minutes per side). Remove pork and set aside.

Braise

Lower heat to medium. Add the quartered onion and smashed garlic to the pot and cook 2–3 minutes until fragrant. Return the pork to the pot, add the stock (enough to come about 1/3 up the side of the meat), cover with a tight-fitting lid, and transfer to a 300°F (150°C) oven. Braise until fork-tender, about 3–3.5 hours.

Shred

Remove pork from the pot and let rest 10 minutes. Use two forks to shred the meat into bite-sized strands, discarding any large pieces of fat. Strain and reserve 1/2 cup of the braising liquid.

Sauce & finishing the pork

In a medium saucepan or the same Dutch oven over medium heat, combine Bulls-Eye® BBQ sauce, Tabasco® sauce, and apple cider vinegar. Add the reserved 1/2 cup braising liquid and stir to combine. Bring to a gentle simmer, then fold in the shredded pork, stirring until the meat is evenly coated and the mixture is heated through (about 5–8 minutes). Taste and adjust heat by adding more Tabasco® if desired (start with the 2 tsp called for). Keep warm.

Grilled pineapple

While the pork is finishing, heat a grill pan or skillet over medium-high heat. Lightly brush pineapple slices with a little oil (or spray). Grill pineapple for 2–3 minutes per side until char marks appear and slices are slightly softened. Remove and keep warm.

Assemble & serve

Split the rolls and spread a thin layer of softened butter on the cut sides. Toast buttered sides in a skillet over medium heat or under a broiler until golden and crisp, about 1–2 minutes per side.

Pile approximately 1/2 cup of the sauced pulled pork onto the bottom half of each toasted roll (adjust to preference). Top the pork with about 2 tablespoons shredded cheddar per sandwich so it begins to melt from the warm meat.

Place one grilled pineapple slice on top of the cheddar for each sandwich. If desired, add an extra drizzle of Bulls-Eye® BBQ sauce or a few drops of Tabasco® over the pineapple for more heat.

Close the sandwich with the top roll, garnish with chopped cilantro or parsley if using, and serve warm.