Taking another look at this, it still seems non-obvious.  I think there are three places where food could be bought in the building: Little Picardy, which has a recent rating that mentions pizza, The Boards pizza restaurant, which I understand to be a separate part of the building (but perhaps shares the same kitchen?), and then the bar -- which I haven't visited and so I don't know whether it offers prepared food or only snacks/prepackaged food.