"amiable stupid person," 1851, from pudding + head (n.). Pudding-face for "person having a fat, round, smooth face" is from 1748.
Entries linking to puddinghead
pudding n.
c. 1300, "a kind of sausage: the stomach or one of the entrails of a pig, sheep, etc., stuffed with minced meat, suet, blood, and seasoning, boiled and kept till needed," perhaps from a West Germanic stem *pud- "to swell" (source also of Old English puduc "a wen," Westphalian dialect puddek "lump, pudding," Low German pudde-wurst "black pudding," English dialectal pod "belly;" also see pudgy).
The other possibility is the traditional one [also in Middle English Compendium] that it is from Old French boudin "sausage," from Vulgar Latin *botellinus, from Latin botellus "sausage" (the proposed change of French b- to English p- presents difficulties, but compare purse (n.)).
The sense of "dish consisting of flour, milk, eggs, etc., originally boiled in a bag until semi-hard, often enriched with raisins or other fruit" had emerged by 1670, from extension to other foods boiled or steamed in a bag or sack (16c.). German pudding, French pouding, Swedish pudding, Irish putog are from English. Pudding-pie as a type of pastry, especially one with meat baked in it, is attested from 1590s.
head n.
Old English heafod "top of the body," also "upper end of a slope," also "chief person, leader, ruler; capital city," from Proto-Germanic *haubid (source also of Old Saxon hobid, Old Norse hofuð, Old Frisian haved, Middle Dutch hovet, Dutch hoofd, Old High German houbit, German Haupt, Gothic haubiþ "head"), from PIE root *kaput- "head."
Modern spelling is early 15c., representing what was then a long vowel (as in heat) and remained after pronunciation shifted. Of rounded tops of plants from late 14c. Meaning "origin of a river" is mid-14c. Meaning "obverse of a coin" (the side with the portrait) is from 1680s; meaning "foam on a mug of beer" is first attested 1540s; meaning "toilet" is from 1748, based on location of crew toilet in the bow (or head) of a ship.
Synechdochic use for "person" (as in head count) is first attested late 13c.; of cattle, etc., in this sense from 1510s. As a height measure of persons, from c. 1300. Meaning "drug addict" (usually in a compound with the preferred drug as the first element) is from 1911.
To be over (one's) head "beyond one's comprehension" is by 1620s. To give head "perform fellatio" is from 1950s. Phrase heads will roll "people will be punished" (1930) translates Adolf Hitler. Head case "eccentric or insane person" is from 1966. Head game "mental manipulation" attested by 1972.