Much has been written about Dame Edna, from her own 1989 autobiography, My Gorgeous Life (which was marketed in Britain as nonfiction), to critic John Lahr’s Dame Edna Everage and the Rise of Western Civilization. Still, nothing prepares you for the actual close encounter. That is because the grist for Dame Edna’s show is not so much scripted material, though there is some, as it is solicitous, utterly terrifying chat with the audience. The star’s maternally couched inquiries run toward babysitting arrangements and decorating schemes — stuff you would not think the most brilliant comic alchemist could spin into gold. Yet Dame Edna is so funny that she has the audience eating out of her bejeweled hand, even when it’s delivering a slap. Of course, her slaps are meant in the most caring and nurturing way. As are her jabs at the poor, the elderly, the variously disabled, and the insufficiently fashion-policed. (She treats political correctness rather like Thanksgiving: we Americans have to observe it, but she, as a tourist, is exempt.)

Dame Edna: The Royal Tour comes to us following a Broadway engagement that garnered a special Tony Award, among other honors. Its titular superstar informs us she would not dream of insulting Bostonians, as in days of yore, with a “tryout”; she broke her show in on Broadway, then took it on the road. Moreover, her glittering vehicle is no ordinary, insulated megahit but a “show that cares.” Pouring wine for a couple she’s invited on stage to have dinner, she crooks her wisteria-hued head in the direction of the next-door Wang Theatre and croons, “Would the Phantom do this?”

So, what exactly does the glamorous icon do? She talks to the audience, both individually and collectively — including an occasional crumb flung to the “paupers” in the balcony. She asks questions, she remembers every name and inconsequential answer, and, boy, does she think on her high-heeled feet. She also, at least on opening night, has phenomenal luck in her addressees (they’re not plants). Looming at the edge of the stage, she picks a young couple to interrogate about their childcare arrangements for the evening. Now, what are the chances that the pair’s tot will be named something as pretentious as “Grayson” or that the babysitter will be from Barbados, a development that allows Dame Edna innumerable sly implications about class in our supposed democracy?

Not one to air-blow her own horn, Dame Edna describes her particular gift as “the ability to laugh at the misfortunes of others.” (She also has a gift for getting others to laugh at the misfortune of those subject to her caring putdowns — so if you don’t want to become material for a megastar, don’t get seated down close.) But what is most striking about the persona, when you consider that Humphries has been channeling Dame Edna since 1955, is how tirelessly he imbues her with energy and slightly cracked pizzazz. Dame Edna: The Royal Tour is a two-and-a-half-hour self-love fest, with only one 15-minute “pause for reflection.” That’s a long time to hold the stage buoyed only by pianist Wayne Barker, two scantily clad “Ednaettes,” a wardrobe on acid, and one’s own rhinestone-obscured balls and quick wits.

You might call Dame Edna an acquired taste that’s been acquired a continent at a time. Australia warmed to the house-proud middle-class wife of Norm Everage (since a martyr to his prostate) when Humphries first launched her in the ’50s, but he couldn’t get Edna arrested in London in the early ’60s. She has been a gender-bent grail in Britain, however, since the ’70s, when she reinvented herself as a superstar. Despite some variously received TV specials, Dame Edna: The Royal Tour seems to have been what put her across in the States.

Not everyone will “get” Dame Edna, with her flat chest and shapely pinions, her sequined frocks and swooping specs, her falsetto stevedore’s blat, and her strange mix of primness, double entendre, malignancy, and megalomania. But if you fall within range of the purring, confiding, querying superstar, watch out. She may or may not be your cup of tea. She’s nobody’s cup of sympathy.