Probably the most exotic burger I've ever eaten is Lesha's "Big Mac Yak Attack" in Langmusi (Langmusi is a Tibetan city on the border of Sichuan and Gansu). Lesha's burger is huge, a giant patty of meat and onions served between two pieces of muslim bread. Not exactly a burger, but the closest thing you will find to one for several hundred miles in every direction. While there also check out Lesha's incredible Apple pie. Darned delicious. This page has photos of yak attack (scroll down to the middle of the page):
http://www.steveamie.com/pages/atrip.htm
Next to this item on the wall reads:
"Many have tried, but failed,
Just eat and compete,
Reduce your plate to zero,
and you'll be a hero."
Google "Lesha yak" for more accounts.