Refers to a hipster threesome involving one male and two females. The reference is derived loosely from the idea of a male tea-bagging one female while the other is sucking the other off to completion. "Earl grey" refers to both the drinks popularity among overeducated, yet nontraditional young people that may be engaged in such an act, and the tea-bagging. The "milkshake" part refers to the males concomitant ejaculation while tea-bagging, making this a really special act.
Mozart was quite kinky, and though they called the act by another lost name, he was one of the first recorded enjoying an earl grey milkshake.