Slice each cuban bread roll in half lengthwise. Spread a thin layer of yellow mustard on both cut sides of each roll.
Layer each sandwich with 2 slices of ham, a generous portion of roast pork, 1 slice of swiss cheese, and 2 lengthwise pickle slices. Close the sandwiches.
Spread softened butter on the top and bottom of each assembled sandwich.
Preheat the air fryer to 360F. Place 2 sandwiches in the basket (work in batches if needed). Place a piece of parchment paper on top of the sandwiches and set a small oven-safe dish on top to press them down.
Air fry for 4 minutes, remove the weight, carefully flip the sandwiches, replace the weight, and air fry for another 3-4 minutes until the bread is deeply golden and crispy and the cheese is completely melted.
Slice each sandwich in half on a diagonal and serve immediately.