Went back to roots today: thinly sliced baked ham & cheese on white with mustard & mayo, but I decided to try a different cheese...
I went to Rome in Sept/Oct, and got a new appreciation for what a good, aged Parmesan can REALLY taste like.  And I bought some when I got home- been shaving it down into various dishes ever since.  Today, it became the cheese on the sandwich.  I was a bit worried, since aged Parm is very dry.  However, the moisture in the mustard and mayo took care of that issue.
I was rewarded with a sandwich with the saltiness of ham & mayo, tang of mustard, and the chewy, nutty flavor of the Parmesan.  This is an experiment worth repeating & expanding.  I can see the Parm working well on a hot bacon-loaded sandwich, for instance.  
It could also go a long way in further "Italianizing" your typical Italian grinder.