George Clooney knows how to get brownie points with his smokin' hot teacher -- by wining and dining her with a super swanky night out on the town.

George and Amal Clooney were out for a romantic dinner over the weekend at Kappo Masa ... a posh Japanese restaurant on NY's Upper East Side.

We're used to the Cloons being the Cloons -- but Amal was at the top of her game too. Columbia University's newest Human Rights Law visiting professor worked the camera ... with a supermodel-esque hair flip.