Make a hole in the middle of both slices; just push the bread to the sides, don't take out any pieces. Put the bread in the panini press and break the eggs into the holes, put some salt on them and mix it up a bit with fingers while spreading it around the bread to cover the entire surface.
Close the panini press untill the eggs are cooked on the outside but not completely solid.
Put cheese [slices] on top of the bread and eggs and put your left over fried food (potatoes in my case) on top of cheese - keep in mind that slices are still separate at this moment.
Close the panini press for about 2 minutes for the cheese to melt a bit as well as for your fried food of choice to press up a bit.
Put one slice atop the other - don't let the fried food fall off of it. Close the press for another 3-4 minutes and it's all done and ready to eat.