For an easy egg sandwich, gather 1 large egg, 1 slice of ham, 2 slices of white bread and 1 tablespoon of butter. Also make salt and pepper available. Brown the bread, and then fry the egg and ham in a large skillet. Build the sandwich with a spatula.
Grease one side of each bread slice with about 3/4 teaspoon of the butter. Heat a large skillet, and place both slices of bread inside, buttered side down. When the butter begins to sizzle, move the bread slices over to one side of the skillet, and add the remaining butter to the other side. Place the ham on the side with the butter, leaving plenty of room for the egg.
Crack the egg inside the skillet next to the ham, and season it with salt and pepper. If desired, pierce the yolk of the egg with a spatula, and let it run inside the skillet. Skip this step if you prefer an intact yolk. After 30 seconds, flip over both the egg and the ham, and allow them to cook an additional 30 seconds. With the spatula, place the ham and egg on the unbuttered side of one slice of bread, then place the other bread slice on top, buttered side up.
Place the egg sandwich on a plate, and serve immediately.