Cook the ground beef in the skillet for 5-7 minutes, stirring often. Carefully drain off about 1/2 the fat and return to stovetop.
Add potatoes, tomatoes and string beans to the skillet and cook for about 8-10 minutes until the potatoes are golden brown.
Transfer to bowl and set aside. Return the skillet to stovetop.
Cook the 4 eggs in the skillet, sunny side up.
Carefully add the potato, tomatoes, string beans and ground beef back into the skillet. Sprinkle in the cheese and cook for about 1 minute.
Salt and pepper to taste and serve the dish right in the skillet.