I made a grilled ham and egg sandwich with cheese for lunch and it turned out pretty good. The egg was hard fried and placed upon some deli ham and toped with American cheese.
The grill pan was preheated for five minutes then the sandwich was grilled on each side for 3 minutes. I used a foil wrapped brick to press the sandwich.
I used a wheat burger bun for the bread. You want something with substance to stand up to the pressing. Regular white bread usually falls apart on me.