We like to use a creamy cheese like Jack or Havarti and a sharp white cheddar (the older the better), equal parts of each is just right. Just about any type of bread will work. Store bought breads usually stay softer, artisan breads will have more of a crunch factor. We like them all. Ok now to the details.
Rough chop a good sized handful of arugula per sandwich and place in a mixing bowl. Drizzle a little Milanese Gremolata EVOO over it, season with a pinch of salt and some fresh ground black pepper. Toss like a salad.
Some add-in options; a drizzle of balsamic, chopped fresh herbs, dried oregano, lemon zest.
Assemble the sandwiches with a nice amount of sliced or shredded cheese, the chopped arugula, and a bit more cheese so that the arugula is covered on both sides.
Brush both sides of the bread with more oil and grill until golden.
Oven grilling work just as well and is a great way to do multiple sandwiches at one time. Just place the sandwiches on a cookie sheet and bake in a pre-heated 375 degree oven for 10-12 minutes.