What a fabulous word fabulation is. Leaving aside the arcane lingo of lit crit, the word means the creation of fables filled with fantasy. Lynn Nottage’s Fabulation, or the Re-Education of Undine creates the fable, and director Lileana Blain-Cruz creates the fantasy in Pershing Square Signature Center’s revival of her early (2004) bold, funny play.

And whoever would have thought to find funny and Lynn Nottage in the same sentence if you knew only her later work, the two Pulitzer Prize winners, Sweat and Ruined, both grim and powerful dramas?

Fabulation is about identity. Undine (Cherise Boothe) is being investigated by the FBI for “identity fraud.” That pretty much describes the last 14 years of her life: Having escaped from the Brooklyn ghetto life she was born into, this woman, originally named Sharona, has won scholarships that gave her access to a posh boarding school and then to Dartmouth, where she read Edith Wharton’s novel The Custom of the Country, about an ambitious social climber named Undine. Sharona renames herself Undine and proceeds to become a ferocious diva of a “boutique PR firm catering to the vanity and confusion of the African American nouveau riche.”

Nottage offers lessons to be learned, most of which we’ve heard before, but this family context — Mother, Father, and Brother are all security guards who love their uniforms, plus there’s a heroin-addicted grandma — is novel, and the satire is too complicated for sit-com laughs, although Social Services takes a hilarious and deserved beating. Not to mention the Yoruba priest with a Harvard MBA.

Once Undine’s Argentine husband, Hervé (their tango has to be seen), absconds with all her money, she finds herself broke, pregnant, and in trouble with the FBI. No place to go but down. Rock bottom turns out to be home. After a heroin bust and a drug rehab circle, she meets a sweet guy (played by the same actor who plays Hervé).

The terrific supporting cast of seven (MaYaa Boateng, Dashiell Eaves, Heather Alicia Simms, Ian Lassiter, Nikiya Mathis, J. Bernard Calloway, and Marcus Callender) play many, many characters, switching accents and costumes and wigs with speed and daring, while Undine narrates developments.

Nottage’s keen eye can create over-the-top stereotypes that somehow ring true, and her keen ear creates wild and sharp dialogue. And it’s always a pleasure to see a playwright range from the tragic to the comic as she tracks women’s lives and predicaments. Her residency at Pershing Square Signature Center will give us a revival of another of her satires, in a very different milieu, By the Way, Meet Vera Stark, beginning performances Jan. 29.

Fabulation, Or the Re-Eductation of Undine. Through Jan. 16 at the Pershing Square Signature Center, The Romulus Linney Courtyard Theatre, 480 W. 42nd Street, New York.