Eat Your Heart Out

As a swanking exultation, a minor singer having just finished a powerful ballad might exclaim, Eat your heart out, Frank Sinatra!' Although current at the end of the last century, this expression acquired popularity in the mid-twentieth century, largely (I would say) through its use in show business circles.

As such, it is another of those Jewish expressions so popularized. Originally, to eat one's heart out' meant simply to pine' and Leo Rosten in Hooray For Yiddish! (1983) suggests convincingly that it is a translation of the Yiddish, Es dir oyss'harts.

Source "Dictionary of Word and Phrase Origins", Nigel Rees