Add the oil to the pan. Crack the eggs into the pan, season with salt and pepper, and cook until the whites of the eggs are firm. Break the yolks and flip the eggs using a spatula, add the cheese. Cook for another minute or until the cheese is melted then place on the bread.
Brown the ham on both sides in the pan.
Place the ham and avocado on the bread. Cut in half and serve with sliced peaches.