Origin and history of pot-au-feu

1640s, "point of convergence," from Latin focus "hearth, fireplace" (also, figuratively, "home, family"), which is of unknown origin. Used in post-classical times for "fire" itself; taken by Kepler (1604) in a mathematical sense for "point of convergence," perhaps on analogy of the burning point of a lens (the purely optical sense of the word may have existed before Kepler, but it is not recorded). Introduced into English 1650s by Hobbes. Sense transfer to "center of activity or energy" is first recorded 1796.

"deep, circular vessel," from late Old English pott and Old French pot "pot, container, mortar" (also in erotic senses), both from a general Low Germanic (Old Frisian pott, Middle Dutch pot) and Romanic word from Vulgar Latin *pottus, which is of uncertain origin, said by Barnhart and OED to be unconnected to Late Latin potus "drinking cup." Similar Celtic words are said to be borrowed from English and French.

Specifically as a drinking vessel from Middle English. Slang meaning "large sum of money staked on a bet" is attested from 1823; that of "aggregate stakes in a card game" is from 1847, American English.

Pot roast "meat (generally beef) cooked in a pot with little water and allowed to become brown, as if roasted," is from 1881. Pot-plant is by 1816 as "plant grown in a pot." The phrase go to pot "be ruined or wasted" (16c.) suggests cooking, perhaps meat cut up for the pot. In phrases, the pot calls the kettle black-arse (said of one who blames another for what he himself is also guilty of) with slight variation of phrasing is by 1650s (a variant with black brows by 1620s in a translation of Don Quixote; older versions also have burnt-arse by 1630s). Shit or get off the pot is traced by Partridge to Canadian armed forces in World War II. To keep the pot boiling "provide the necessities of life" is from 1650s.

1923, type of Vietnamese soup, probably from French feu "fire" (for which see focus (n.)) "as in pot-au-feu, a stew of meat and vegetables of which the broth is drunk separately as a soup" [Ayto, "Diner's Dictionary"] which would have been acquired in Vietnamese during the French colonial period (ca. 1858-1945.) See also pot-au-feu.

PHO [...] is made with beef, a veal bone, onions, a bayleaf, salt and pepper, and a small teaspoon of nuoc-man, a typically Annamese condiment that is used in practically all their dishes. [...] To go with this soup special kinds of noodles are made with flour, egg and water.

[Countess Morphy, Recipes of All Nations, 1923.]

The Encyclopedia Britannica adds, without dismissing the feu theory, that it "appears just as likely that the dish’s name evolved from the Vietnamese pronunciation of the Chinese fen, which means 'flat rice noodle.'" However, rice noodles do not appear to be present in many early versions (including the above recipe) which raises doubts about this derivation.