Fry eggs until yolks are set. Split bread into slices and layer salami and ham with egg and cheese on the bottom slice.
Top your sandwich with the other slice of bread and toast on a Panini grill or indoor grill until the bread is toasty and the cheese is melted. The trick is not just to grill the bread, but to press it as well.
If you don’t have a sandwich press, use a well-greased fry pan to cook the sandwich and use a bacon weight or a heavy pan to press the sandwich until the bread is crisp and the cheese is melted.