Prepare everything before heat is applied. Cut the pork into even pieces so it cooks at the same pace. Slice the yellow onion, mince the garlic, and keep the red onion separate for the garnish. In a small bowl, combine smoked paprika, cumin, chipotle, salt, pepper, and brown sugar. Pat the pork dry thoroughly, then coat it with the spice blend. This is critical: dry meat browns; damp meat steams. In another bowl, mix the barbecue sauce, stock, tomato paste, and apple cider vinegar until smooth. Finally, dress the sliced red onion with half of the lime juice and a pinch of salt; let it soften while the pork cooks.