Here’s what I’ve learned from my experience:
-Agree with the tomato comment. Thinly sliced is sometimes better for heat transfer. Heirloom if you can get ‘em. Beefsteak for volume. You can also grill them first, and add them to the sandwich before you grill it. You can also add red grilled peppers, sauted portobello mushrooms, or a combination of all of these, although then it’s straying away from a strict “cheese” sandwich. (also, all three makes the sandwich pretty slippery. With tomatoes I try to layer cheese and tomato to avoid losing the slices. Use the melted cheese as a kind of adhesive.
-softer cheeses are better. They have lower melting points. Muenster is absolutely excellet in this regard, but it has a very mild and buttery flavor. Cheddar is pretty great at melting quickly, and packs a punch.
-sourdough develops a really great “soft” crunchy quality. Thinner breads tend not to transfer the heat to the cheese, and get really hard and rough on your mouth by the time you’re done cooking the sandwich.
-Cooking the sandwich for a longer time on lower heat gives the cheese a chance to melt without burning the bread. Also, adding a lid over the pan helps trap heat and encourage melting. Of course, this is not the route to take if you’re really hungry and want food imediately.
-experiment with spices. Spanish smoked paprika adds a meaty flavor.