Sam Gold's revival will also star Maggie Gyllenhaal and Cynthia Nixon.
The fantastical comedy is the Long Island theater's next offering.
Bertolt Brecht's The Caucasian Chalk Circle and Tom Stoppard's Arcadia round out the season of premieres.
The revival is also set to star Maggie Gyllenhaal and Ewan McGregor, both making their Broadway debuts.
Carey Perloff will direct the Tony Award winner in this off-Broadway premiere.
The theater will also present world premieres of Carey Crim's Conviction and Adam Overett's My Life Is a Musical.
The organization will also showcase Tom Stoppard's Indian Ink and The Real Thing next season.