It seems to me that Thompson kind of works her way down the most important Oz characters that Baum didn't give title novels to, and fills in those gaps. Relatively early in her tenure, we got The Cowardly Lion of Oz, then Hungry Tiger. Now we get Jack Pumpkinhead of Oz, I kind of suspect because Thompson had to reread Marvelous Land in order to write Giant Horse. It probably stuck out to her that not only had Jack Pumpkinhead not had a title role yet, he'd scarcely had a line of dialogue in the preceding twenty-one books!

Like most Oz novels, though, it's focalized through a human child, so Jack Pumpkinhead brings back Peter from Gnome King. Peter was gifted a sack of pirate gold by Ozma before he returned to America at the end of Gnome King; here he discovers that the sack is magic and it contains a magic coin. The coin is magic change, and thus gives Peter a magic change, whisking him to Jack's house in Oz. The two set off for the Emerald City, but because Jack isn't the brightest, they go the wrong way and end up in the Quadling Country where they have a series of adventures, some totally standalone, but mostly revolving around trying to stop an evil baron from capturing the Emerald City.

I enjoyed it, and I think my four-year-old son did too. It recaptures for me what is the essential Oz formula: a group of unusual people who become friends and solve problems together as they cross through an unusual landscape. Peter and Jack are joined by Snif the Iffin (he was a griffin, but he cannot growl anymore and thus has lost his gr) and Baron Belfaygor, whose attempt to grow a beard before his wedding resulted in a fast-growing beard that just will not stop. The four have to work together to stop Baron Mogodore of Baffleburg from kidnapping Belfaygor's fiancée, Princess Shirley Sunshine, and attacking the Emerald City. There's a lot of creative problem solving, mostly revolving around various ways to make use of Belfaygor's beard, as well as a magic dinner bell the characters acquire during their travels. I don't think it will set your world alight, but it does exactly what an Oz novel ought to: good jokes and fun characters and suitable fantasy perils.

Jack even gets a nice, clever hero moment. This is something Oz authors don't always do for their title characters; the Scarecrow contributes nothing to the resolution of Scarecrow of Oz, for example! But as we near the climax, Peter, Belfaygor, and Snif are all taken out of commission, so it's Jack on his own who is responsible for saving Oz, with a characteristic clever piece of Thompson wordplay.

(The problem with Oz books is that it is pretty hard to justify why Oz needs saving when it is ruled by a fairy princess surrounded by magical advisors, and the explanation in this one is pretty contrived, but to be honest I was entertained, so that's fine. The Emerald City is captured because Ozma and her friends happen to be playing blind man's bluff at the exact moment Mogodore and his army arrive!)

A couple other thoughts:

• Perhaps the various barons in the Valley of the Barons are some of the people Grampa fought against in his 980 battles (as per Grampa in Oz).
• Based on what Baron Mogodore gets up to here, one feels that maybe Glinda should be reading her Great Book of Records more often to find out what crimes her subjects are committing.
  
• It's a very male adventuring party. It's not the first Oz book where all the adventurers are male (or at least male-coded): see Marvelous Land and Cowardly Lion for other examples. But this group stuck out to me more than those, I guess because Peter is very much a boy's boy, loving sports and adventures, which isn't true of, say, Button-Bright or Ojo. On top of that, Belfaygor is questing to rescue a princess help captive in a tower. Surely a most masculine pursuit!
• We read this in October, which was very seasonally appropriate: not only is it about a jack o'lantern, but Peter and Jack meet Snif in Scare City, which comes across as a haunted house.
• This book is the first appearance of Jinnicky the Red Djinn, who is a pretty minor character here, but will go on to appear in a number of Thompson's novels.