Spread mustard over 2 slices of bread; top each with cheese slice, ham, pulled pork, pickled jalapeño slices and another cheese slice. Spread mayonnaise over remaining slices of bread; cap sandwiches. Butter outside of sandwiches.
Preheat panini press according to manufacturer’s instructions. In two batches, grill sandwiches for 2 to 3 minutes or until bread is toasted and cheese is melted.