There's an interesting little shop called Dosruk in Tokyo that serves Uygur cuisine from the Xingiang Uygur Autonomous Region of far western China. I've never been to that region, but I think the food here might be pretty authentic, and they do have a native Uygar chef. The food is very different from Chinese in its spices and flavors, and it's based heavily on lamb and mutton. (There was a travel book at the restaurant that showed people roasting a whole baby camel on a spit, but they didn't have that on the menu here in Tokyo.) I had some excellent chewy white noodles with lamb sauce; they were unmanageably long, but I was given a pair of scissors to cut them with before serving. The menu also offers mutton and potato stew, lamb kebabs, roast lamb, boiled sheep's tongue (with red pepper and garlic - very tasty), and sheep's stomach. Plus lots of soups, side dishes and starters, all quite cheap. The setting itself is no-frills noodle-shop, with plastic tablecloths and a TV set going in the corner, but the food is good and very reasonably priced.
Dosruk. 03-3354-8542. Open 5:30pm-1:30am (LO). Closed Mondays. Shinjuku 6-13-8. (The shop is a bit hard to find, in a semi-residential neighborhood between Higashi-Shinjuku and Shinjuku 3-chome stations.)