The other side is convex and looks similar to this side. I found it with my V3i in a grassy field that dates back to the 1940's. I have found relics from the 1800's and early 1900's there as well. This item was buried about 9" on edge like it crashed, spinning into the dirt.
Probably hit the dirt when the whiskey still blew. They hammered out a lot of eating and cooking utensils back then. That size would be about right for the bottom of a pitcher or cup but without more you may never know.
I had a friend once who had a water sculpture on their front porch that had plates similar to yours. It was a fountain that had copper leaves that simulated lily pads. Maybe something along that line but I don't have any photos to prove my theory.
Thanks for the answers everyone. This particular park has been extremely productive. Most of the large pieces I have dug there have been trash, so this one was interesting enough to keep.