a la mode......Beef and ice cream

[Sam Clements]

So, we've taken "pie a la mode" back to 1895.  I have no doubt that it goes
back farther.  But can anyone truly tell me what it was?

If  "beef a la mode" wasn't a piece of stewed cow with a scoop of tutti
fruti on top, then why was "pie a la mode" a piece of pie with a scoop of
ice cream on top?  How do we know that the pie didn't have cream poured over
it, and this was considered "in the manner?"  When did the ice cream become
the "mode?"  Any cites before 1920?