Clean, wash, and dry the chicken breast steak, for example using kitchen paper towels.
Place the chicken steak between two pieces of plastic wrap and pound it with a meat mallet to about ½ inch thickness.
Salt and pepper the meat on both sides.
Melt the butter in a pan over medium heat. Place the prepared chicken steak in the melted butter, increase the heat slightly and fry the meat on both sides until golden on the surface.
In the meantime, prepare the peach: depending on its size, halve or quarter it and place it in a home grill/toaster to bring out its flavor.
Remove the pan with the finished chicken steak from the stove. Place a slice of cheese on top of each steak. Cover with a lid and let the cheese half melt.
Arrange the chicken steak with melted cheese on a plate, top with a peach, and serve with boiled potatoes. Pour over the juices from the bottom of the pan that was produced during the cooking of the chicken.