During the swing era , his big band was popular with hits like `` Begin the Beguine '' ( 1938 ) , `` Stardust '' ( with a trumpet solo by Billy Butterfield ) , `` Back Bay Shuffle '' , `` Moonglow '' , `` Rosalie '' and `` Frenesi '' .
During the Swing Era , his big band was very popular with hits like `` Begin the Beguine '' .