So what to expect of her now? “If it’s more trauma, I’m fresh out,” Gadsby quips onstage. “Had I known just how wildly popular trauma would be, I might have budgeted mine better. I could have had a healthy trilogy.”

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Instead, Gadsby created “Douglas,” the new show she’s touring (her four-week, off-Broadway run starts July 23) before Netflix releases it in 2020. She struts out to Madonna’s transcendent karaoke anthem, “Like a Prayer.” She greets the crowd under a giant goofy photo of her and her fluffy dog, Douglas (yes, she named the show after him). And she explains exactly what she will do: I will tell some traditional stand-up jokes and needle the patriarchy; I will say some serious sentences and purposefully refrain from making them funny; I will deliver a literal lecture and it will be enjoyable; and you will be surprised by my single Louis C.K. joke, even though I’ve already told you I’m going to tell one.

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Gadsby essentially makes several promises, and then she sets about making good on them all.

Two hours later, the comedian has traded her blue suit for a casual blue jacket and pants — she always wears the color, it helps calm her — and while sipping from La Croix backstage, still has energy to talk for one more hour. Whereas performing “Nanette” could drain her, “Douglas” leaves her buoyant.

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“To follow on from ‘Nanette,’ this is the other side of trauma,” she explains. “Like I’m able to have a genuinely good time onstage. I’m having fun with this show. . . . There is another side of life if you can deal with your trauma, which is not easy, because we focus on trauma instead of focusing on what can happen after.”

Gadsby, 41, only wrote “Douglas” in March, but the themes have been steadily stewing in her mind: the names we give things and the limits they carry, what is considered genius and why we are so certain.

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“What I want essentially is flexibility of form. That’s what I’m driving at,” Gadsby says, noting “flexibility is seen as a feminine trait and it’s seen as a weakness.”

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Gadsby already began playing with stand-up conventions in “Nanette,” launching a discourse about post-comedy and whether something like “Nanette” should even be considered stand-up. By using comedy’s tools — timing, building tension, callbacks — Gadsby set out to break the genre itself.

She sees that comedy has always coexisted with tragedy — one cannot thrive without the other — and that upholding laughter as the king in comedy can be dangerous.

“The premise of skill is not the same as having something to say. Why make people laugh, why are we doing this? People will laugh, they’ve got this,” she says. “It’s very arrogant to think we need comedians if laughing is the only reason they’re there, because everyone knows how to. We got it.”

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“By making comedy not funny, I’m turning comedy into a joke,” she continues. “The reason we make jokes about things is either to hold up power or disrupt it, and that was a disruption of power.”

The effort was met with massive praise as soon as “Nanette” hit Netflix. Overwhelmed, Gadsby put her social media away for a week after the premiere before she eventually hit the talk-show circuit in the United States, presented at awards shows and made famous friends.

Up until that point, Gadsby had a well-established career in Australia and understood what “buzz” could look like, “but then I found out what a ‘buzz flood’ was.” The flood also carried debris: When she returned to social media, she discovered some very real hate directed at her once it was clear that her special had struck a chord.

“Douglas” was “always going to be a push back on people who didn’t like ‘Nanette,’ not because I think they shouldn’t, but because their reaction wasn’t about ‘Nanette,’ ” she says with a laugh. “So that fascinated me.”

Gadsby talks of haters in “Douglas” with the inquisitiveness of a researcher and tackles the rigidity of genre and historical narratives. Who made the decisions as to what’s worth remembering and who belongs in the canon? Not women, she argues; history is “men’s mood diary.”

“Douglas,” which does include a heart-wrenching moment, conveys more joy than what American audiences associate with the comedian. Gadsby issues an invitation into how her mind functions, as she discusses being on the autism spectrum. Even the show’s structure is a reflection of her idiosyncrasies: She sees it as a bunch of hexagons that she is figuring out how to fit together, with each piece offering six possible ways to match with another.

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Instead of callbacks, Gadsby laces the show with “call forwards,” which renders what would otherwise be silly jokes actually quite complex. She incorporates slides of artwork, and loves inventing self-imposed rules, such as one that prevents her from adding more paintings to the show to add more jokes. “But I’m allowed to search in the [existing] paintings and find the bits,” she explains.

Although Gadsby mentions him briefly in “Douglas,” Louis C.K. — who admitted to sexual misconduct allegations in 2017 and promised to stop performing and listen for a while — is treated as an abstraction and counterpoint to her work. His fall coincided with her rise, and many of her haters make up his fan base, she says. “Men will literally say to me, ‘At least Louis C.K. is funny. You had to be raped to be relevant.’ You know, things like this. It is horrific.”

Initially, Gadsby refrained from commenting publicly on C.K. because he had “some healing to doing and some thinking to do.” Then nine months after going silent, he began performing again and Gadsby said his leaked set — in which he mocked the Parkland, Fla., shooting survivors, using a derogatory term that Gadsby finds especially horrendous — demonstrated a “complete lack of empathy.”

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“I don’t want to make light of why he made those decisions,” she says of his sexual misconduct, “but he is making light of it by not thinking it through. So he’s given me permission to go, ‘You’re a joke until you learn why this is not acceptable.’ ”

While Gadsby thinks of herself as an outsider who doesn’t care much about the state of comedy in the United States, her presence here represents a challenge. Those who cry “free speech” but are threatened by her commenting on a powerful man in the industry are missing the point, she says; comedy is “the little guy having a voice.” And to her, the worry that “political correctness is going to kill comedy” is a sign of weakness.