1) Toss together pork and 2 tablespoons of the barbecue sauce in a bowl until fully coated. Sprinkle lower half of each tortilla with 2 tablespoons of the cheese. Top evenly with pork mixture and onion slices. Sprinkle evenly with remaining cheese. Fold each tortilla over filling.
2) Heat a large nonstick skillet over medium; coat with cooking spray. Working in batches, if needed, add quesadillas to skillet; cook until golden brown on both sides, about 2 1/2 minutes per side. Remove from skillet.
3) Cut each quesadilla into thirds and divide among 4 plates. Drizzle evenly with remaining 2 tablespoons barbecue sauce. Top evenly with sour cream and jalapeño slices; sprinkle with cilantro. Serve immediately.