In a small bowl, toss the pulled pork with the BBQ sauce until evenly coated. Warm it in the microwave for 1-2 minutes if it is cold.
Butter one side of each slice of sourdough bread. Place 4 slices butter-side down. Layer each with 1 slice of cheddar cheese, a generous mound of BBQ pulled pork, pickled red onion if using, another slice of cheddar cheese, and the second bread slice butter-side up.
Preheat the air fryer to 360F. Carefully place 2 sandwiches in the basket and air fry for 4 minutes.
Carefully flip the sandwiches and air fry for another 3-4 minutes until the bread is deeply golden and crunchy and the cheese is fully melted and gooey. Repeat with remaining sandwiches.
Let rest for 1 minute, then cut in half diagonally and serve while the cheese is still stretchy and hot.