Marty Gleeson @ Pleasance Courtyard

Dog Ear, the fascinating debut from Marty Gleeson, is surely due a Best Newcomer nomination. Gleeson's distinctive comic voice is partly about her actual voice – deep from an early age apparently, imbuing schoolyard chat with a threatening edge. Partly, though, it's her skewed perspective and offbeat, dead-eyed tall tales. Gleeson brings an unusual kind of authority to the show, as she coolly inspects the audience, and pads thoughtfully about the stage.

Born and bred in Limerick, her primal scenes establish the place as something of a crucible for hard men (at a disco for 12- to 14-year-olds, the smoking areas are packed with hardened kid smokers) but also a kind of integrity, too. Gleeson went to art school but tells us it's a less precious, privileged matter in Limerick: if you can draw an anatomically correct horse, you go to art school.

Some sequences start with conventional enough shapes; believing in Father Christmas too long as a child or watching yoga videos on YouTube, but each spins out into surreal territory. She likes to push a bit to breaking point – she riffs on her name sounding like an old geezer's, and imagines him playing chess with Gabe, his elderly mate, a man who looks like a turtle, then escalates to the funeral service for her dead geezer self. And suffice it to say, we really see that service through.

There's a sequence about multiple David Attenboroughs laying eggs; an 8ft magpie; exploding Demodex, the tiny mites that live in our pores. It's hard to pinpoint what's so intriguing about Gleeson's approach – the stand up conventions of crowdwork, picture props and callbacks are present and correct – but in her hands it all feels new.

Gleeson likes being a stand-up. 'We can do anything', she says contemplatively, and on the evidence of this, she's probably right.

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Marty Gleeson: Dog Ear, Pleasance Courtyard (Bunker One), until 30 Aug (not 17 Aug), 7.15pm, £11.50-14.50