Here's a hint, above. Yes, it's a pepper mill!
The mill is made of pieced teak with an iron handle and has a lovely soft patina from what I can only guess to be many years of use. It's easy to operate: you simply turn the handle and out comes the pepper from the bottom. To refill you just pull out the red plastic plug and pour in your peppercorns.
I've done some poking around online and have found similar vintage pepper mills, usually paired with a twin salt mill, by Nissen for Bodum. My mill does not have any Bodum markings on the bottom, but it does say Peugeot on the grinder. The internets also say that this teak wood version is rare, although those claims are usually on sites that are also trying to sell it.
Since the pepper mill comes with the apartment, I won't be selling it but I have enjoyed using it. It's got a pleasing weight, fitting very nicely in my hand, and produces a nice, even, fine grind. My only complaint is that there are no adjustments for medium or coarse grinds.
(Images: Dana Velden)