The Collaborative International Dictionary of English v.0.48:

borsh \borsh\ n. [Yiddish borscht, fr. Russian]
   a Russian soup usually containing beet juice as a foundation,
   and often served with sour cream. Also, as used in the U.S.,
   a sour cabbage soup, called in Russian shchi.

   Syn: borsch, borscht, borsht, borshch, bortsch.
        [WordNet 1.5 +PJC]

WordNet (r) 3.0 (2006):

borsh
    n 1: a Russian or Polish soup usually containing beet juice as a
         foundation [syn: borsch, borsh, borscht, borsht,
         borshch, bortsch]