I found this at a thrift shop today. I have no idea what it may be, but it looked like one of those allusive range accessories that someone is always pining after (like me and my Frigidaire probe)
It looks like the Jenn-Air deep fryer. You can see the marker on the side for the oil level. It sits on the grill elements so there is no thermostatic control. There is one for sale on eBay. Yours looks better and you probably got it cheaper. Congratulations. Tom
Actually now that I look at it again, I see that yours has 'woodtone' handles with different end-pieces. Mine has black handles. Perhaps it was available both ways.
Thanks for clearing up the mystery! I knew there would be folks here who could ID it.
So, here's the next question: Anybody out there need a Jenn-Air deep fryer? I would be happy to have Santa send it to you, and will even go back to the thrift store and see if the extra parts are floating around.
If no one wants it, I'll probably donate it back so a local Jenn-Air enthusiasts can find it.