This may be the ultimate rabbit hole. New York Public Library’s collection of 17,562 menus ranging from 1850 to the 2000s have been digitised and are available here.
They are also in the process of extracting all the dishes from those menus to make a searchable index by dish rather than establishment name. So far, 1,335,578 dishes have been transcribed. The are looking for volunteers to assist with this project.