Green’s Dictionary of Slang

tenement house in Greenwich Village n.

[play on SE greens/Greenwich]

(US) an order of soup with greens in it.

[US]N.Y. Herald 1 Apr. 9/6: During his stay in the restaurant the reporter learned several things he never knew [...] That ‘a tenement house in Greenwich Village’ meant a plate of soup with plenty of greens in it.