CALF’S HEAD AND FEET—illustration from The Royal Cookery Book (Le Livre de Cuisine) (London: Sampson Low, Son, and Marston, 1869), by the French chef and pâtissier Jules Gouffé (1807-1877):

 

The earliest occurrence that I have found of the obsolete British-English phrase (a) calf’s head is best hot, also calves’ heads are best hot, is from Slang. A Dictionary of the Turf, the Ring, the Chase, the Pit, of Bon-ton, and the Varieties of Life, Forming the Completest and Most Authentic Lexicon Balatronicum * Hitherto Offered to the Notice of the Sporting World (London: Printed for T. Hughes, 1823), by the British author and journalist Jon Bee (John Badcock – fl. 1810-1830):

‘Calf’s head is best hot,’ was the apology for one of those who made no bones of dining with his topper on.

(* The adjective balatronicum was derived from the Latin noun bălātro/ōnis, which denoted a babbler, hence a jester, a buffoon. This noun was in turn derived from the verb blătĕro, to talk idly or foolishly, to babble, prate.)

The second-earliest occurrence that I have found is from History of George Godfrey. Written by himself (London: Henry Colburn, 1828), a novel by the English novelist and journalist Thomas Gaspey (1788-1871):

“Julius Cæsar, was ordered into ‘durance vile.’ He did not forget his manners, however, for the moment this decision was pronounced, having heard that ‘a calf’s head is best hot,’ he put his caster on his sconce, in the presence of Sir Benjamin.
“This contemptuous conduct on his part, astonished all present. Sir Benjamin directed the officer to remove it, which was done, evidently to the infinite displeasure of Julius Cæsar, either for the reason before surmised, or from a conviction that one of his great name, ought not to submit to the humiliation, of standing uncovered before such humble individuals, as a Magistrate and Baronet, and a Peer of the realm.
“The hero retired in the custody of an officer, but was afterwards bailed.”

The phrase then occurs in the account of the speech that George Faithfull, M.P., delivered during the public dinner given to the Representatives of the Borough of Brighton on Tuesday 10^th September 1833—account published in the Brighton Guardian (Brighton, Sussex, England) of Wednesday 11^th September 1833:

(Mr. Faithfull was here importuned to put on his hat, which he declined doing, observing in the most facetious manner, that “calf’s head was best hot!” After this digression on this head, the speaker proceeded thus, [&c.]

The earliest occurrence of the plural form calves’ heads are best hot that I have found is from a letter to the Editor, published in The Bury and Norwich Post, and East Anglian; or, Suffolk, Norfolk, Essex, Cambridge, and Ely Intelligencer (Bury St Edmunds, Suffolk, England) of Wednesday 31^st December 1834:

I happened, Mr. Editor, to be leisurely walking about the town, when my hand was suddenly seized, and most familiarly shaken; and before I could recover the surprise, the gentleman had nearly doffed his hat, and with it his wig. I pressed him to keep on his hat, and my usual presence of mind enabled me to hint, “that calves’ heads were best hot”—the adage, I acknowledged, was stale.

The plural form then occurs in the column Tittle Tattle, published in The Era (London, England) of Sunday 28^th June 1846:

Calves’ Heads are best Hot.—It has been found necessary to fix a notice on the doors of the parish church of Halifax, requesting that men would keep off their hats whilst within the walls of the church.

Finally, the following is from The Western Times (Exeter, Devon, England) of Saturday 20^th October 1849:

The Cap of Condemnation.—The respected public writer, who is familiarly known as the heavy man, puts on a black cap, when, like Sir John Falstaff, he goes from tavern to tavern, in order to show the farmers the folly of seeking a reduction of rent. When apologizing for covering his skull, he was pleasantly reminded, that it was a prudent precaution, as “calve’s [sic] head was best hot.”