Thanks once again to George Motz for the tip on this one - there are several of these stands around Nashville, but I'd never made it to one before. The burger tasted just like the ones I used to get at the Middle Eastern delis while in college in Knoxville, TN (i.e. there's some weird spice mix in there that I can't quite place).
My burger:
The sign for the 27-oz 'Supper Deluxe:'