Bear with me on this. I’m usually Mr Memory, right, but I can’t recall the last time I saw a Broadway musical where the leading lady gets to play a woman who has an affair with her gynaecologist when several months pregnant. He calls her into his office early in the morning on the pretext that “light spotting” calls for another examination. If the way to a man’s loins is through his stomach, this musical – with its attractively earworm-infested score and lyrics by Sara Bareilles – is in no hurry to dispel this myth. Jenna, our working class Southern heroine (beautifully played by Katharine McPhee) works as a waitress at Joe’s Pie diner and is a dab hand at baking those extravagant American confections that could give you a coronary, were you simply to pronounce their names. polka dot peach pie is about as restrained as it gets.

This is both a romcom set in the workplace and a feminist drama in which the protagonist makes painful progress to the belatedly assertive moment when she boots out her smugly abusive husband (he takes it for granted that her tips belong to him and seizes automatic control of them as if he were her pimp). Admittedly, there are moments of discomfort but it says a lot for the fast sass and wonderful take-it-or-leave-it silliness and the occasional sugar-free sequences in Jessie Nelson’s deft book that the spot-on cast in Diane Paulus’s production mostly manage to give these elisions an elating good humour and humanity.

Over at the diner, Jenna has the supportive friendship of two fellow-waitresses – Marisha Wallace’s Becky, who mischievously tries to be as big of heart as of voice, and Laura Baldwin’s petite, twitchy Dawn. One doesn’t tend to get dramatised in the musicals of Rodgers and Hammerstein; you can hunt the length and breadth of The King and I and not find even the semblance of a predictor-stick. They arrange things differently in Waitress. Our trio break into song about Jenna’s predicament in the Ladies and there’s a very funny joke where one of the diners is about to confuse two rather different forms of utensil. The songs grew on me; they are in a pop idiom over an intricately figured rhythmic floor (one of these reminded me strongly of the Batman theme). It’s as if their staying power feels as if it’s being epitomised to the point of satire in the number “Never Ever Getting Rid of Me”. This latter is sung by the hilarious Jack McBrayer as Ogie, who becomes the slapstickily persistent admirer of Dawn. They bond over American War of Independence reenactments which bring out their libido in ways of which Martha Washington might not approve. I would kill to be a fly on the wall if they ever audition for Hamilton.

I should declare an interest. Up hill or down dale, I have never knowingly refused a piece of cake. I have three daughters and tend to wobble a bit during songs where mothers sing to the daughters they are thinking about at the time. There is one in Mamma Mia that unmans me (to put it at its most feminist) so badly I have to leave the room and consequently can’t remember its title. There is a brilliant example in the second half of this show where Jenna tries to explain herself to her not-yet-born baby. It’s devastating because of the utter dignity with which McPhee invests it.

The acting is very skilled. David Hunter is Dr Pomatter, the gynae with the beside manner that seems to have been choreographed by a department of cartoonists. But then he’s also plausibly romantic in a soaring act two diet. Kelly Agbowu is delectably amusing as his nurse who gets more and more pissed off as he sends her on increasingly pointless tasks so as to give him and Jenna some privacy. You might think that the show is going to climax in a Stateside equivalent of Bake Off (which is overdue a musical makeover) but actors who feel it is their destiny to play Paul Hollywood on the boards, can breathe freely again. I’m not prepared to spoil things by spelling it out, but thing don’t work out in the way you have been led to expect.

The stage is flanked by two of those all cabinets from which cakes ogle out at you. That’s reasonably funny. I was less sure about the baking aromas that hit the nostrils at the back of the auditorium and in the foyer. These don’t seem all that authentic to me and put me in mind of being shown round houses, as a prospective buyer, by people who have sprayed their properties in bogus bread-baking deodorant. The show, though, is the real deal.