The first thing to know about Amazon Prime's The Marvelous Mrs Maisel is the name of the woman who created it, Amy Sherman-Palladino. If that name gives you an inexplicably autumnal feeling — maybe you can suddenly hear the faint strains of a Carole King song wafting through your mind — it's probably because you've seen it a hundred times before during the opening credits to Gilmore Girls.

Her new show, a comedy-drama set in New York in the 1950s, shares a few of the characteristics that made Gilmore Girls such a rare treat for its legions of fans. For a start, if you've seen even one episode of that show it should come as no surprise that The Marvelous Mrs Maisel is, to use the technical term, extremely talky.

Everybody on this show loves to talk and they are all very good at it because if there's one thing Sherman-Palladino knows it's how to write dialogue that makes her characters appear superhumanly quick-witted. The one exception to the good talking rule is Mrs Maisel's husband Joel (Michael Zegen), a sub-Mad Men uptown New York office worker who, once a week, dons a black turtleneck and heads downtown to perform his stand-up comedy routine on open mic night at The Gaslight.

In short, he's a total hack; his whole sorry routine is stolen from a comedian he saw on TV. Still, consummate 1950s housewife Miriam "Midge" Maisel (Rachel Brosnahan) indulges his delusions of comedy grandeur, dutifully attending every session, taking notes on his set ("You got three more laughs than you did last time, and a couple of extra laughlets") and bringing a Pyrex full of brisket as a bribe for the owner to give her ungrateful husband a better time slot.

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But that's not even what makes Mrs Maisel so marvellous. The show is about what she does next, after he leaves her for his secretary the night before Yom Kippur. First she drops the kids with her hysterical (and hysterically wealthy) parents, then she cracks into the special holiday wine and rides the subway to The Gaslight to pick up her Pyrex. Three sheets to the wind, she stumbles on to stage and accidentally performs an impromptu stand-up set that sets the wheels of an unlikely career in comedy in motion (and gets her arrested for public exposure — nothing tells the audience you're a serious TV show like a bit of nudity in the first episode).

After all, she's already got a notebook full of joke ideas and a Yoda-like mentor in The Gaslight server Susie (Alex Borstein, the voice of Lois on Family Guy). How hard could it be for a 1950s housewife to make it in the world of comedy?

Brosnahan is excellent as the show's complex and compelling lead, making Midge an instant pleasure to watch and root for. The impeccable set and costume design holds up its end of the bargain too — like the romantic snowglobe world of Gilmore Girls' Stars Hollow, the New York of the show is a joy to spend time in, glistening in a way that probably isn't a hundred per cent historically accurate, but never mind — it isn't meant to be a documentary.

The Marvelous Mrs Maisel is for fans of Gilmore Girls, regardless of how you felt about the revival. It's for fans of Mad Men who miss all the stylish mid-century interiors. It's for anyone with room for a quality, fun new TV show on their viewing schedule.

• The Marvelous Mrs Maisel is streaming on Amazon Prime Video.