By "slow-cooking" do you mean braising, or using sous-vide?
Most restaurant, to my knowledge, offer some version of a braised meat. The shortribs at Lucques, pork shanks at Literati II, the shortribs at Hatfield's are some that come to mind.
As for sous-vide, I know that Hatfield's uses that method for their halibut, and Sona uses it also for various dishes. BTW, sous-vide is a method of cooking where you vaccuum seal the food item and slow simmer it.
Chili My Soul in Encino, CA proudly boasts that their chilies are all cooked for 40+ hours (they have about three dozen chilis in rotations of 10--always a few without beans and at least one vegetarian.) It's generally good but with so many varieties, there are bound to be hits and misses (thank goodness for free samples.)