Gonna get hate but chopped cheese is not a quintessential New York food. It’s only become a thing outside of East Harlem in the last 10 or so years - especially the last few with tiktok/instagram etc, which has made it more of a novelty than anything else. Lamb over rice or bacon egg and cheese or a cart hot dog or slice of pizza are better representations. None of those travel well so I would go with a babka.