When Laura Benanti was 4 years old, she listened to the music of the original cast album of My Fair Lady and decided that one day she would play Eliza Doolittle, who goes from flower girl to belle of the ball. “It’s absolutely true,” she swears before an evening performance at Lincoln Center. “It’s my dream part since I was 4. I’m not exaggerating.”

Her dream — which was on the verge of fading at the age of 39 — came true when director Bartlett Sher asked the Tony Award-winning actress (Gypsy) to succeed Lauren Ambrose of New Haven in the role in the hit revival of the musical.

“When they first talked of reviving the show, my daughter was 5 months old and they were asking everyone to audition,” she says. But Benanti decided her daughter was too young. “I just let it go. Then Bart called me and said Lauren was leaving the production because she got a television show.”

Benanti, who will be singing in concert at the Long Wharf Theatre gala June 3, got the part and is having a ball — and going to one at every performance. “I feel much more comfortable in my motherhood and my daughter, who is 2, understands what I do for a living now. She’s able to come to the theater between shows and has seen me in the show — at least the first act.”

Like Ambrose, Benanti is an older Eliza than originally written “but in this day and age, the story of an older man and a much younger woman whom he’s grooming for a wife is not the story we want to be telling,” she says. “As an older Eliza I can bring layers to this character that [I] would not have been able to do at 18 because I didn’t have the life experience. So I’m grateful to be playing it at this age with what I know now.”

Benanti also starred on Broadway in the revival of She Loves Me, Steve Martin’s Meteor Shower and the musical Women on the Verge of a Nervous Breakdown. Her Long Wharf show, Tales from Soprano Isle, which is separate from the gala and open to the public,will include songs from her career and stories from her life on and off the stage. Her musical director is Todd Almond, whose musical Girlfriend is playing at Hartford’s TheaterWorks through April 28. Maybe she’ll even do a bit of Melania Trump, a character she plays every once in a while on CBS’s Late Show with Stephen Colbert.