A breakfast sandwich refers to any kind of sandwich filled with foods that are usually considered a breakfast staple such as cured meats, eggs, cheese, and various types of bread. Before the explosion of breakfast sandwiches in the United States, they were often consumed by factory workers of the 19th century London, where they were called bap sandwiches, named after the soft (and back then, often slightly stale) rolls filled with fried eggs, crispy bacon, and melted cheese.
During the industrial revolution, the breakfast sandwich became popular in the USA, filled with eggs, green peppers, onions, and ham. It was a staple of blue-collar workers, and the first recipe can be found in a cookbook that was published in 1897.