Two slices of Sharp American. On a mushroom burger, like the others, a good Swiss.
I like blue cheese on my salad, not on my burger. I do sell a lot of bacon & blue burgers with grilled onions & horseradish mayo though, so it is popular on burgers.

Beef and blue cheese are a popular combination. I don’t however get it. I find they compete rather than compliment.
 
DT