A real puzzler. The seller lists some guesses,
but none seem likely to me.

http://www.ebay.com/itm/160799433505

Whatever goes in the cup can't be too tall,
or it will hit the handle. It can't be
on fire, or it will get soot on the handle
and heat it up. The fact that the cup swivels
suggests it holds a liquid or maybe a powder,
the swivel action to keep it from spilling.
Maybe it does spill sometimes, hence the dish.