Puddinghead

...this is a beautifully made example of protective headwear worn by children in the early 19th century. Pudding caps or bumpers were padded hats commonly worn by small children learning to walk to protect their heads from any falls. It was thought that if children fell too frequently unprotected their brains would turn to a soft pudding-like consistency, hence the name "pudding cap." Children were often referred to as "little pudding heads" because of this belief.

Finally I understand the reason for the name of Mark Twain's character "Puddn'head Wilson" (perhaps the term was explained in the book - I don't know).

From the Brooklyn Museum Costume Collection at The Metropolitan Museum of Art, via A London Salmagundi.

Addendum:  BJN makes an excellent observation:

"Pudding" in England derives from small sausages, and even today the term applies to a wide range of foods, not just the creamy desserts that Americans refer to.

The entry at Victoria & Albert shows a pudding cap [~1775-1800] and describes the hat's name thus; "The nickname of ‘pudding’ comes from the padded roll’s similarity of shape and size to the type of sausage called ‘pudding’, a popular food still eaten today."

I think it's more likely that the idea of soft brains is a later Americanism and it's probably more of a humorous tongue-in-cheek use than a literal belief.

That makes complete sense to me.

And, for completeness, here's the relevant quote from the first chapter of Twain's book:

"Yes, sir, he's a dam fool. That's the way I put him up," said No. 5. "Anybody can think different that wants to, but those are my sentiments."

"I'm with you, gentlemen," said No. 6. "Perfect jackass -- yes, and it ain't going too far to say he is a pudd'nhead. If he ain't a pudd'nhead, I ain't no judge, that's all."

Mr. Wilson stood elected. The incident was told all over the town, and gravely discussed by everybody. Within a week he had lost his first name; Pudd'nhead took its place. In time he came to be liked, and well liked too; but by that time the nickname had got well stuck on, and it stayed. That first day's verdict made him a fool, and he was not able to get it set aside, or even modified. The nickname soon ceased to carry any harsh or unfriendly feeling with it, but it held its place, and was to continue to hold its place for twenty long years.

Obviously, by Twain's time (1893 for this book), in the U.S. the term was being used to refer to brain damage.