The best way to improve on a great grilled cheese is to sprinkle some cheese on the outside of the bread for a super-crisp, cheesy crust. Switch up the ordinary with this Grilled Ham and Cheese Sandwich. A simple addition helps our Grilled Ham and Cheese Sandwich stand out from the crowd. Our take on the classic grilled sandwich includes Swiss cheese, arugula and sourdough bread. Grilled Ham and Cheese Our take on the classic grilled sandwich includes Swiss cheese, arugula and sourdough bread. No matter what time of day it is, a skillet toasted ham and cheese sandwich made with Sargento® Sliced Medium Cheddar Cheese, tangy Dijon mustard and. This gooey mess of caramelized onion and barbecue sauce also tastes great as a cold sandwich. (And did you know caramelized onions freezes well?.