We’ve had the impossible girl, the girl who waited, the shop girl who did and the doctor who didn’t, and of course the Doctor’s “mate”. But for the first time probably in its history, Doctor Who has embraced a woman writer who has managed – in spite of the absence of an actual travelling companion for the greater part of its duration – to get inside a female character’s head in a way that the series has only ever hinted at before. That Maisie Williams’ gender was the least important aspect of the story, signalled perhaps in the opening sequence, was particularly impressive, allowing Catherine Tregenna’s script to deal with the issue at hand (the absence of Clara, in every possible meaning of that sentence) in a uniquely feminine, but distinctly not feminist, way.

In spite of the reflecting titles, The Woman Who Lived was the least clear second half of a two-parter this series, including as it did – and just like last week’s episode – an entirely discrete plot, around which the characters’ story could be told. And yet it was easily the most satisfying even-numbered episode of Series Nine, largely because rather than continue the plot but try and confound expectation by taking it in an unanticipated direction, the fact that the situation and monster-of-the-week had changed allowed Tregenna to fulfil all the story strands left hanging over from The Girl Who Died without repeating any of the previous episode’s beats. It was like watching The Long Game the week after Dalek and not feeling deflated by the experience. Some pleasantly relaxed pacing, a pretty innocuous alien plot, occasionally laboured comedy and a couple of clunky slo-mo shots and ill-advised line readings were all reminders of what last week’s episode did better, but whereas last week was a lip-smacking aperitif, here we had the main course, and if it let itself down slightly in some peripheral areas, perhaps that’s what it took to get the story of the Doctor and Lady Me into a rewarding but still entertaining 45 minutes.

The pacing was rather like an elongated tango, often gliding almost to a stop for the Doctor and Ashildr (sorry, Lady Me)’s head to heads before sliding back into the jocular set pieces that pushed the story along, but beautifully presented and always gorgeously shot; some of the character studies in the filming and lighting felt like they’d been teased out of a feature film budget. Tregenna’s script was an antithesis of The Girl Who Died, hanging a deliberately slight yet organically formed alien invasion – that used the hand-me-down plot points from last week in often unpredictable but entirely natural ways – in order to give the substance of The Woman Who Lived room to breathe, and all the more apt because of it. That Tregenna managed to keep the interactions of the main players flowing throughout both the allegro and andante, so that the story unfolded across the entire composition rather than in fits and starts throughout, created a harmony of vision that allowed for most of the episode’s more wilful digressions. Rufus Hound’s Sam Swift the Quick might have felt utterly out of place in another production of this story, but here he was entirely in keeping with the Shakespearian shifts between bawdiness and profundity, and even precipitated the episode’s one moment of true pathos. If he was this year’s Frank Skinner, then he made a stand-up job of it.

Maisie Williams herself was perhaps rather less successful, embracing her character’s emotional core but with an occasionally wooden delivery – something she mostly avoided in the previous episode. Not that it mattered overmuch; Ashildr was compelling enough without any dramatic fireworks flying about, and Peter Capaldi (looking evermore like Graham Crowden in Waiting For God whenever he smiles) continues to become a more and more likeable Doctor, even as his performances improve in their unpredictability and assurance. It was fantastic to see an actor who is so accomplished embracing the role, and it’s astonishing to see him still improving after such a fine beginning in Deep Breath.

And when Jenna Coleman finally turned up, she was delightful and light and natural and charming; all the more so because if The Woman Who Lived was anything, it was the story of the disaster that awaits Clara Oswald – as told through the prism of a woman who is the current companion’s opposite in almost every way. Ashildr’s line about how many Claras the Doctor has lost, or her appearance in the background of a pupil’s selfie at the end of the episode, made the trajectory of the arc most apparent, but what we had here instead was a reading of that arc in microcosm; an antithetical analogy for what’s been happening throughout Clara Oswald’s engagement with the Doctor, and an indication of where it must be heading. Where the Doctor conferred immortality on Ashildr, he very ostentatiously refused to do the same for Clara, perhaps because he foresaw how problematic it might be (or maybe because he remembers her splintering throughout his timelines and thus already having achieved a kind of immortality that way); where he refused Ashildr’s beseechments to take him with her, he goes back for Clara time after time after time; where Ashildr sees only the most cynical aspects of the world around her and seeks escape, Clara sees the world as a place of wonder to be investigated; and where Ashildr is saved by the eventual resurrection of her compassion, leading her to a place of calm acceptance, Clara is no doubt heading towards tragedy because of the way she throws herself into her “hobby”. This was a story that could only be told in the absence of Clara, without the character getting under the feet of it, and without making the parallels too obvious by her interaction with them.

Catherine Tregenna achieved all of this while simultaneously telling a story about the Doctor’s immortality and about how for him, that immortality is a facilitator for good, whereas in less assured hands it could be a curse and a catalyst for a transgressive existence. Replete with insight, and yet never unbalanced at the cost of the entertainment, Tregenna’s first Doctor Who episode is a singular agglomeration of elements that should never work collectively, and yet not only do, but dance a consummate and entirely unique rhythm across the screen. That she has included a deeper understanding of the Doctor than we’re used to, freed from the superficial nature of some other writers’ occasionally cursory character observations, alongside a multi-layered discerning of a guest character that reflects both him and his companion back at once, and all in 45 minutes, is rather special. If there are a few small sacrifices required in order to achieve that, then so be it; you don’t get an episode like this along every week, and we should cherish that Steven Moffat, even after six years of broadcast Doctor Who, is still willing to push at the boundaries of what the series should be.