how about a sausage on a roll? Is that a sandwich? Hmm.

Wikipedia and I think so. Perhaps the definition might include the "eaten from the hand' phrase along with 'a filling surrounded by bread of some sort'. That would tie in with the habit of that eponymic father of the thing. That would also let in the hotdog and the meat ball sandwich as well as all the po' boys, subs, heroes, et cetera, et cetera and so forth.