NEW YORK — Here’s a Barbara Cook fun fact: She’s gaga for Hugh Jackman. As in crazy, over-the-moon, can’t-get-enough-of-him enraptured. “When he did ‘Oz,’ I saw it 16 times in New York,” she confesses, recalling Jackman’s Tony-winning turn in the 2003 musical “The Boy From Oz.” She notes that when she was visiting Sydney, she made a bunch of additional pilgrimages to the show there: “Six times in four days,” she boasts.

“Seeing Hugh is like going to church,” Cook explains, sitting in her homey Upper West Side apartment, chockablock with Native American and African pottery — another of her passions. “Because he is such a spiritual person. There’s no way you’d know this about him, but he’s one of the most profoundly good people I’ve ever known. He has a perfectly fine voice, but it’s about his willingness to show us who he is that is so moving. He allows himself to be so vulnerable.”

Cook has launched into a Jackman testimonial — hey, who’s winning the award here? — as she rhapsodizes about her good fortune in receiving the Kennedy Center Honors. She was hoping, she says, that Jackman would have been available to help fete her Sunday night, when the center tapes its annual, star-engorged tribute. Alas, Jackman sent word that he couldn’t leave his own show “Hugh Jackman, Back on Broadway,” one of the fall’s hottest tickets.

Cook, who turned a gob-smacking 84 on Oct. 25, says she understood why he couldn’t make it, but she also wants to, ahem, clarify his appeal for her. “So many people say, ‘Oh, you’re in love with him!’ ” the singer observes. “I’m not in love with Hugh Jackman. ‘Oh, it’s because he’s so sexy!’ No, that’s not really it, either.

“Here’s the thing: What I try to tell students in master classes is what we want is them. It’s so hard to believe that what the world wants is the intrinsic you on the stage. And that’s what Hugh Jackman’s got, in spades. He’s incredibly present.”

The same, of course, can be said for Cook. With her immaculate natural instrument and the ebulliently permeable sense of self she projects in her concerts, she’s the empress of “present.” “Everybody’s on her team,” says Jessica Molaskey, the musical-theater actress who with jazz guitarist-husband John Pizzarelli developed a cabaret act, for which Cook has been a mentor. “She’s an exquisite musician, and she just happens to have the most shimmering luster. Her voice has a quality that shimmers. And I haven’t seen it go away.”

Jackman, for his part, considers Cook “the greatest living example of acting through song.”

“Her technique is extraordinary, and she allows me to forget that I am an actor, and to just be a fan,” he says. “I first saw her giving a master class in Melbourne, and, to be honest, I consider every subsequent performance that I have seen her in as a master class.”

Though the Honors more often than not go these days to artists of both achievement and a certain magnitude of celebrity, Cook’s overdue selection is not one being relied on to boost the telecast’s ratings. She’s from an even more rarefied circle of recipients, those who earn a coveted seat in the president’s box based essentially on their art alone. Having begun her career as an ingenue in Broadway musicals, she gravitated during a rocky midlife to a second act as an interpreter of show tunes and other standards — the concert and cabaret existence for which she’s now more widely recognized. Such an eternally fresh, expressive exemplar of the form is she that when the Kennedy Center decided to establish in 2007 an ongoing series of evenings featuring the nation’s best cabaret singers, it asked Cook to serve as its talent scout and curator.

Her durability, too, is a little bit freakish. How is it that a woman who made her Broadway debut in 1951 (in a flop called “Flahooley”) and is the resonant soprano on the original vinyl recordings of “The Music Man,” “Candide” and “She Loves Me” can in 2011 still be a supple source of musicality? Cook attributes her longevity to first-rate training: “In 1953, I got with the teacher who built my voice, Bob Kobin,” she says, sitting in her living room overlooking Riverside Park, seeming relaxed in black slacks and black turtleneck.

He instilled in her a comprehension that if properly used, the voice would last. “He used to say the vocal cords are among the strongest things in your body,” Cook says, adding that she’s a firm nonbeliever in wrapping the throat in scarves and all that pampering stuff. It’s learning how to manipulate the muscle that counts. “You can forget about hot tea and lemon, too,” she says, with a dismissive wave.

Anyone who’s seen Cook in concert would feel an immediate kinship with this disarmingly forthcoming woman in her art-filled home: She’s identical in temperament to the person on the stage who dips into the songbooks of Rodgers and Hammerstein, Stephen Sondheim, Duke Ellington and Irving Berlin. The candor with which she talks about herself — about the psychological cruelty she endured in her mother’s Atlanta home, her early struggle with the meaning of success and a subsequent descent into alcoholism — is of a piece with the entertainer who approaches her performances as acts of accessibility.

She’s open, too, about the opportunities missed, especially as they regard broadening her renown. (After two screen tests, she lost the part of Marian the Librarian in the movie version of “The Music Man” to Shirley Jones and since then has had a virtually nonexistent film career.) “It’s not that I wouldn’t have liked it,” Cook says, “but I think I’ve wanted to keep my life simple, and that has not always worked out in my favor. I would have been wiser to have fought more for TV and film.”

No one would confuse her concertizing for a confessional, but the absence of artificiality on these evenings has become a hallmark. Even in the potentially fraught predicament of dropping a lyric (which has been known to happen), she’s able to acknowledge, shrug off and metabolize the mishap. That’s, literally, the voice of experience.

“I’m more comfortable with who I am. I’m more comfortable on a stage. I’m more comfortable with putting myself in my work,” she says of the evolution of her life as a performer, during an afternoon-long conversation. “When you allow people to really, really see your humanity in its most profound form, it touches that humanity in them. In that critical way, we find we’re not so alone in the world.”

The confidence that comes with so pure an attention to rhythm and pitch — “She sings in the middle of the note,” marvels Molaskey, who appeared in Cook’s cabaret series with Pizzarelli — is no doubt an advantage to a singer seeking to cross emotional bridges through melody. For Cook, that translates into finding meaning in a composer’s original intent, rather than trying to improvise a new one.

“She serves the songwriter while being true to herself as a performer,” says Alexander Gemignani, a New York actor-singer who was flattered to have been approached by Cook to perform in her Kennedy Center series.

Her life and career have been based in New York for more than 60 years; she married and later divorced David LeGrant, who died several years ago; their only child, Adam, lives in Manhattan. And always, her work has revolved around the sounds she makes, from her earliest gigs, when she sang on bills with legendary groups such as the Weavers.

Along the way, she’s developed an appreciation of vocalists of eccentric range: Her enthusiasms include not only role models such as Ella Fitzgerald and Rosemary Clooney, but also Jimmy Durante and Lady Gaga. The performer who made the deepest impression, however, was another celebrated cabaret singer: Mabel Mercer. All of these names are linked in Cook’s imagination by the gift she attributes to Jackman: evoking an authentically complete portrait of oneself through song.

She prizes this consummate ease above technique, though many of her idols had that, too. “When I saw Mabel, I bought what she sold immediately. I thought it was thrilling and exciting. And I wanted to do that.” Her inspiration, she says, “all came from Mabel — well, nine-tenths Mabel and one-tenth Judy Garland.”

In the midst of writing a memoir, Cook finds herself rummaging in some less tantalizing corners of her past. She traces a painful relationship with an overbearing mother to a horrible interlude: her sister’s death in childhood from whooping cough, an illness she’d overheard her mother say was contracted from Cook herself — which Cook had long taken to mean she had killed her sister.

About her drinking, Cook says it became a daily ritual for her, in the years after the juicy roles and Golden Age of Broadway musicals disappeared. “Let’s face it, I’d get drunk every night,” she says. And it continued for a spell even after she formed a professional partnership in the mid-1970s with Wally Harper, the composer and musical director who was instrumental in Cook’s rebirth as a concert singer. It was Alcoholics Anonymous that helped her get sober, and her flourishing cabaret life with Harper continued until his death in 2004.

Now, she says, she carries with her a vigorous sense of joy, whether for her own gigs or the performances of people she likes. “I read an article about Baryshnikov giving boxes of videos” of his dancing to the New York Public Library for the Performing Arts, she says, “and he was asked why he didn’t sell them. ‘Selling my life? I do that in the theater!’ he said. That’s what I’m doing. I’m sharing with an audience my life, the good and the bad.”

The sharing goes on and on. This 84-year-old, for goodness’ sake, has just released a CD, “You Make Me Feel So Young.” And can’t get over being elevated to the Kennedy Center pantheon.

“I feel clearly that it’s a validation of my work,” she says. “And because I put my life into my work, I think it’s a validation of my life.”

See the rest of this year’s Kennedy Center Honorees:

Meryl Streep | photos

Neil Diamond | photos

Sonny Rollins | photos

Yo-Yo Ma| photos