In French cookery, the feminine noun madeleine denotes a small rich cake baked in a fluted tin, which gives it a shell-like shape. It is first recorded in the plural as Magdeleines, in a list of petits fours published in Almanach des gourmands (Paris, 1807), by Alexandre Balthazar Laurent Grimod de la Reynière (1758-1827).

It was originally gâteau à la Madeleine, cake in the manner of Madeleine. The reason for the designation is dubious. In Néo-physiologie du goût par ordre alphabétique, ou dictionnaire général de la cuisine française ancienne et moderne (Paris, 1839), Maurice Cousin, comte de Courchamps (circa 1777-1859), attributed the invention of the recipe to a certain Madeleine Paumier, “pensionnaire et ancienne cuisinière de madame Perrotin de Barmond” (“lodger and former cook of Mrs Perrotin de Barmond”), of whom nothing is known.

(English Maudlin, the popular form of the name Magdalene, probably originated in French forms such as Madeleine.)

The term gâteau à la Madeleine is first recorded in Les Soupers de la Cour, ou L’art de travailler toutes sortes d’alimens (Paris, 1755):

Gâteaux à la Madeleine.

Sur une livre de farine, il faut une livre de beurre, huit œufs blanc & jaune, trois quarterons de sucre fin, un demi-verre d’eau, un peu de citron verd [sic] rapé, ou citron confit haché très-fin, fleurs d’orange pralinées ; paîtrissez tout ensemble, & en faites de petits gâteaux, que vous servez glacés de sucre.

It first appeared in English in The Professed Cook: Or, The Modern Art of Cookery, Pastry, and Confectionary, Made Plain and Easy (London, 1767), the translation by B. Clermont of Les Soupers de la Cour:

Gâteaux à la Madeleine. Common small Cakes.

To a Pound of Flour, put a Pound of Butter, eight Eggs, Yolks and Whites, three Quarters of a Pound of Sugar-powder, a Glass of Water, a little Lemon-peel, chopped very fine, dried Orange-flowers; work it well together; then cut it in Pieces, of what Bigness you please, to bake, and glaze them with Sugar.

In English as in French, madeleine is used figuratively to mean an object or a sensation which makes pleasant memories resurface. It is a literary reference to Du côté de chez Swann (1913), in À la recherche du temps perdu (In Search of Lost Time), by the French novelist, essayist and critic Marcel Proust (1871-1922). The taste of madeleine cake soaked in tea brings back the narrator to his childhood past:

(from Swann’s Way – 1922 – translation by Charles Kenneth Scott Moncrieff (1889-1930))
And suddenly the memory returns. The taste was that of the little crumb of madeleine which on Sunday mornings at Combray (because on those mornings I did not go out before church-time), when I went to say good day to her in her bedroom, my aunt Léonie used to give me, dipping it first in her own cup of real or of lime-flower tea. The sight of the little madeleine had recalled nothing to my mind before I tasted it; perhaps because I had so often seen such things in the interval, without tasting them, on the trays in pastry-cooks’ windows, that their image had dissociated itself from those Combray days to take its place among others more recent; perhaps because of those memories, so long abandoned and put out of mind, nothing now survived, everything was scattered; the forms of things, including that of the little scallop-shell of pastry, so richly sensual under its severe, religious folds, were either obliterated or had been so long dormant as to have lost the power of expansion which would have allowed them to resume their place in my consciousness. But when from a long-distant past nothing subsists, after the people are dead, after the things are broken and scattered, still, alone, more fragile, but with more vitality, more unsubstantial, more persistent, more faithful, the smell and taste of things remain poised a long time, like souls, ready to remind us, waiting and hoping for their moment, amid the ruins of all the rest; and bear unfaltering, in the tiny and almost impalpable drop of their essence, the vast structure of recollection.

In Homes Sweet Homes (London, 1939), the English cartoonist and author Osbert Lancaster (1908-86) wrote, about English interior decoration:

Late in the period conversation pieces were allowed provided the personnel were carousing Cardinals. Generally speaking the only alternative to oil paintings as a form of wall decoration were steel engravings, preferably by Monsieur Doré, of sacred subjects. (It should never be forgotten that the dining room of the period had taken over some of the functions of a private chapel in that it was invariably the scene of family prayers.)
So lasting were these traditions that the childhood memories of many still comparatively young retain their ineffaceable impress. Thus the sight of a Van der Velde seascape still brings the taste of mulligatawny whistling up from the author’s subconscious while the flavour of Bordeaux pigeon summons with all the completeness of Proust’s tea-soaked madeleine an unforgettable cloud of Mons. [= Monsieur] Doré’s angels hovering over the Colosseum.

In The Big Time, a review of two books, The Lawless Decade by Paul Sann and George Hornby, and The Perils of Prosperity 1914-1932 by William E. Leuchtenburg, published in The Spectator (london) of 1^st August 1958, D. W. Brogan used madeleine without explicit reference to Proust:

We all have our little fragment of madeleine that brings back a dearly remembered but half-forgotten past, and mine was provided not by the rumbustious authors of The Lawless Decade but by the more sober, academic work of Professor Leuchtenburg. For it was the Professor who quoted the Gaudeamus igitur of the era of The Girl Friend: he brought up from my submerged memories ‘Collegiate,’ and all, or nearly all, came back. ‘Collegiate, collegiate, nothing intermediate,’ that was the spirit of the epoch which was nominally presided over by Messrs. Harding and Coolidge, the epoch in which I first set timid steps upon American soil, the era of the big bonanza, of the last, great, carefree explosion of 100 per cent. Americanism, the last period in which God’s People and God’s Country were believed to be exempt from the ills that deservedly befell more sinful lands and when there were few evils that a few laws, usually promoted by formidably righteous women, would not cure.