The prefix out- has been used to form verbs such as outbid, outdo, outlive and outnumber, which convey the sense of surpassing, exceeding or beating in the action described by the simple verb.

The phrases built on the pattern to out-X X—in which X is a person’s name—mean to be superior to X in his or her characteristics.

For example, in The Tragedie of Hamlet, Prince of Denmarke, as published in Mr. William Shakespeares Comedies, Histories, & Tragedies. Published according to the True Originall Copies (London: Printed by Isaac Jaggard and Edward Blount, 1623), the English poet and playwright William Shakespeare (1564-1616) used to out-Herod Herod ¹, meaning to be superior to Herod in cruelty, evil, extravagance, etc.:

Enter Hamlet, and two or three of the Players.
Ham. Speake the Speech I pray you, as I pronounc’d
it to you trippingly on the Tongue: But if you mouth it,
as many of your Players do, I had as liue the Town-Cryer
had spoke my Lines: Nor do not saw the Ayre too much
your hand thus, but vse all gently; for in the verie Tor-
rent, Tempest, and (as I may say) the Whirle-winde of
Passion, you must acquire and beget a Temperance that
may giue it Smoothnesse. O it offends mee to the Soule,
to see a robustious Pery-wig-pated Fellow, teare a Passi-
on to tatters, to verie ragges, to split the eares of the
Groundlings: who (for the most part) are capeable of
nothing, but inexplicable dumbe shewes, & noise: I could
haue such a Fellow whipt for o’re-doing Termagant ²: it
out-Herod’s Herod. Pray you auoid it.

¹ Herod the Great (c.74-4 BC) was the ruler of ancient Palestine from 37 to 4 BC. According to the New Testament, Jesus was born during his reign, and he ordered the massacre of the innocents. He was represented in the miracle-plays as a blustering tyrant.
² In A General Glossary to Shakespeare’s Works (Boston: Dana Estes and Company, 1904), Alexander Dyce explained: “Termagant (a Saracen deity, at least such according to the crusaders and the old romance-writers) was, like Herod, along with whom Shakespeare here mentions him, a character in our early Miracle-plays.”

Among the phrases built on the pattern to out-X X is to out-Zola Zola ³, meaning to be superior to Émile Zola in Naturalism.

³ The French novelist and critic Émile Zola (1840-1902) was the chief exponent of Naturalism, a 19^th-century literary and artistic movement, influenced by contemporary ideas of science and society. The members of this movement believed that the writer or artist should apply scientific objectivity and precision in observing and depicting life, without idealising, imposing value judgments, or avoiding what may be regarded as sordid or repulsive.

These are the earliest occurrences of the phrase to out-Zola Zola that I have found:

1-: From The Sporting Times (London, England) of Saturday 3^rd May 1879:

Wilkie Collins ⁴ has evidently read the “Mysteries of Paris” ⁵ to some purpose, seeing that in his story now being published in the World he introduces Fleur de Marie, under the name of Simple Sally, to his readers. Possibly we shall be treated with second editions of the schoolmaster and the screech owl, as the author of the “Woman in White” excel [sic] Eugene Sue in horrors, and out-Zola Zola in realistic effects.

⁴ Wilkie Collins (1824-1889) was a British novelist and playwright. His fifth novel, The Woman in White, was first serialised in Charles Dickens’s journal All The Year Round, starting in November 1859; it established what became known as sensation fiction: novels written to provoke a strong emotional response in the reader, depicting lurid, shocking or thrilling material. Simple Sally is the name of a character in Wilkie Collins’s novel The Fallen Leaves, first serialised in The World, starting in January 1879.
⁵ First serialised in the Journal des débats, starting in June 1842, Les Mystères de Paris (The Mysteries of Paris) is a novel by the French author Eugène Sue (Marie-Joseph Sue – 1804-1857); la Goualeuse, a 16½-year-old prostitute, has been nicknamed Fleur-de-Marie (slang for the Virgin) because of the virginal ingenuousness of her features.

2-: From Theatricals, published in the Weekly Dispatch (London, England) of Sunday 1^st June 1879:

Prominent among the new pieces is Mr. Charles Reade’s ⁶ adaptation for the Princess’s of “L’Assommoir,” ⁷ to which has been given the suggestive title of “Drink.” This remarkably sensations drama has already been adapted in New York, where it has caused no less excitement than in Paris. Theatrical managers are quarrelling everywhere for the sole right of performance—a distinct proof of their faith in the public appetite for the morbid and the horrible. The original play is a satire on human nature, and its moral is stern and relentless; and Mr. Reade’s version, it is reported, will out-Zola Zola in its realistic delineation of some ugly and ghastly phases of life. There can be no question that those who love to have their feelings harrowed when they visit the theatre have a treat in store for them.

⁶ Charles Reade (1814-1884) was a British novelist and playwright.
⁷ L’Assommoir (1877) is the seventh novel in Émile Zola’s series of twenty novels collectively entitled Les Rougon-Macquart: Histoire naturelle et sociale d’une famille sous le Second Empire (1871-93). In L’Assommoir, Gervaise opens her own laundry-shop and for a time makes a success of it; but Coupeau, her husband, squanders her earnings in the Assommoir, the local drinking shop; Gervaise too slides into heavy alcoholism, and the couple gradually sink into poverty.

In the following from the column Diary, by Alan Rusbridger, published in The Guardian (London and Manchester, England) of Wednesday 2^nd May 1984, a variant of the phrase to out-Zola Zola alludes to J’Accuse…! (I Accuse…!), the title of an open letter that Émile Zola wrote to Félix Faure (1841-99), President of the French Republic, published on Thursday 13^th January 1898 by the newspaper L’Aurore (Paris), condemning the imprisonment of Alfred Dreyfus (1859-1935), a French artillery officer of Jewish descent whose trial and conviction in 1894 on charges of treason caused a major political crisis in France:

Mr Oliver Miles ⁸, our late man in Libya, last saw his children’s pet rabbit—Honeybun by name—on the back lawn of the British Embassy at Tripoli. She was nibbling the grass.
The rabbit has caused Mr Miles some discomfiture since then; in particular, since her plight was advertised in a newspaper. “I’ve had over a dozen abusive hate letters from the Great British public about Honeybun,” he disclosed mournfully yesterday. “The letters seem to assume that all Libyans are bad, and that it was therefore cruelty to leave her behind.”
But what of Honeybun since? It is said that the Mail on Sunday, in an effort to out-Zola its sister paper, has flown Honeybun home. Certainly, a rabbit has arrived from Tripoli on a British Caledonian flight to Gatwick and has been impounded by the relevant authorities, lacking, as it was, the appropriate paperwork. The authorities are unimpressed by the argument that the rabbit should be accorded diplomatic immunity.
The fate of the rabbit is now being considered at Departmental level. Nothing, surely, that a phone call to Leon Brittan ⁹ won’t sort out?

⁸ Oliver Miles (1936-2019) was the British Ambassador to Libya in 1984.
⁹ Leon Brittan (1939-2015) served as Home Secretary from 1983 to 1985 in Margaret Thatcher’s government.