Tig Notaro knew just how to conclude her newest comedy special. She would show viewers a road trip gone tragically bad. There was a crucial step to create the scene, though: She would need the cooperation of Dolly Parton.

“I was a little nervous because she’s such a perfect human being that I was scared she would be like, ‘I don’t know if I want to be part of this bloody mess,’ ” Notaro says by phone about using the singer’s likeness and her self-pity-spun-into-bliss ‘70s tune, “Two Doors Down.” But because Team Parton signed off, “I now think they’re even cooler than I ever did — and that’s hard to top.”

Then again, who doesn’t want to work with Notaro right now? She hasn’t stepped on a standup stage in a year and a half because of the pandemic, yet her career grows only more multifaceted: The L.A.-based comedian and actor recently flew to Toronto to shoot for her series “Star Trek: Discovery”; she’s traveled to New York to judge film festivals; she made her action-hero feature debut in a new Zack Snyder film; and she keeps two freshly launched podcasts going strong (when not co-parenting young twin sons).

And Saturday, she’ll make her debut as a fully animated comedian. Her hour-long cartoon standup special “Tig Notaro: Drawn” comes to HBO and HBO Max as an experimental mix of observational humor, offbeat visions about pop icons and deliciously skewed tales that craft punchlines out of pain.

Not that Notaro, 50, planned her early pandemic schedule this way. When the nation went into lockdown, she stayed close to home. “I just wanted to be very safe — I’ve had some major bumps and setbacks with my health over the past nine years,” says Notaro, including breast cancer, a double mastectomy and a life-threatening intestinal infection. Her brave 2012 “I Have Cancer” standup performance at the L.A.-area club Largo, shortly after receiving her diagnosis, went viral — spotlighting a deadpan honesty that elevated her fame and became entwined with her persona.

For this new special, Notaro’s singular voice also sharpened one of her favorite bits of medical material: “When people say, ‘Where are your boobs now?’ I always say, ‘Probably in a dumpster in an alley in Hollywood somewhere.’ ” She didn’t think to include that onstage aside in her suggestions to the special’s director, Greg Franklin, but he discovered it when listening to hours of her live-performance audio. “He loved that so much and wanted to animate this,” Notaro recounts. “I was like: ‘Great, put it in! I love saying that to people.' ”

Notaro and Franklin, co-founder of the Six Point Harness animation studio, wanted to work together more than a decade ago, but no studio or network was interested in backing their cartoon concept. Three years ago, ready to revive the idea, she asked Thomas Ouellette, an executive producer on the special, to cull through dozens of hours of Largo performance audio to see what could work. And last year, Notaro found herself in a surreal setting, poised to pitch this experiment again.

She says she sold the project to HBO “the day that Hollywood shut down” — in March 2020.

“I remember a very eerie feeling — there weren’t many people there,” she recalls of sitting in the offices of HBO, which had begun sending workers home. “In fact, I was pitching to the network executives on Zoom — I was in the offices and they were on Zoom.”

The scores of artists and animators nimbly worked around the constraints of quarantine life. “It was crazy that we were able to take this audio and animate it — from our phones and home offices — with just everybody locked inside,” Notaro says.

Early on, Notaro also thought that the pandemic could imperil her standup career — a possibility her spouse, writer-actress Stephanie Allynne, initially pooh-poohed. “It took her about a year to realize I wasn’t kidding,” the comic says. (Notaro is still on “high alert” about safety amid the pandemic; she just booked a movie shoot and feels more comfortable with on-set covid-19 protocols than touring on the road.)

As Notaro and her collaborators worked on the special, the full meaning of its title was fleshed out. It is “not just that I’m drawn with a pencil,” she says — it also reflects being fatigued and physically drawn. She says they decided to steer toward some of her medical material from several years ago: “I’ve kind of been forced to time and time again find humor in these rough moments.”

Visually, the show plays out like only loosely connected scenes, each rendered in a distinctive style — from line drawings to retro character designs to 3-D modeling evocative of a modern kids’ show. We see young Tig playing a school talent show or imagining that Eddie Van Halen is spying on her through the woods (she cried the day he died). We see an adult Tig end up at the emergency room or bleeding profusely after dental surgery. We get a breezy riff about the wall-crashing antics of the Kool-Aid Man, and we see how a series of unfortunate events for Notaro leads to her repeatedly canceling a meetup with fellow comedian Jenny Slate. “She’s a very kind and great person. Who on Earth wants to get sucked up in that hell when you’re just trying to have tea with somebody?” the performer says of the story’s comedic conceit.

“Tig Notaro is a brilliant storyteller, and since animation is a traditionally narrative medium, we could structure this special with numerous distinct styles that fit each bit thematically,” says Franklin by email, noting that the shifting styles heighten viewer surprise.

“While there is always an impulse to cram as many visual jokes on screen as humanly possible, the ebb and flow of the material comes from Tig’s mastery of timing,” adds the director, who was animation supervisor on the Oscar-winning “Hair Love” and “The SpongeBob Movie: Sponge Out of Water.” “So as animators, we are allowed to let the audience wallow in hilariously awkward beats and milk that tension for all it’s worth.”

Notaro, meanwhile, thinks all the differing cartoon depictions of her aptly reflect the “many sides to my comedy.”

From “the health scares and the observational side of me,” plus “the silliness and sincerity and connecting with the audience,” she has her own verdict about finally making the special: “That was fun.”

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