Chopped cheese is a New Yorker sandwich originating from Harlem and The Bronx. It is made by stacking ground/chopped beef and onions, melted American cheese, lettuce, tomatoes, and condiments on a hero roll. The sandwich became something of an underground, subcultural cult over the years among the locals.
It originated in the bodegas in East Harlem, and it is believed that Hajji's is the first bodega that started to sell this sandwich. Chopped cheese is probably an adaptation of an Arabic sandwich called dagha yamneeya, and it's no wonder, considering that many bodega managers come from Yemen.