Green’s Dictionary of Slang

cheek, audacity, nerve.

1867		Sportsman 14 Dec. 2/1: Notes on News [...] What would be the result of a thorough investigation of the stuff covered by his [i.e. an preacher’s] own ‘crust.’ Bad enough surely, if wo may judge from the blasphemous, bigoted, and blatant steam the pie gives forth.
1900		E.H. Babbitt ‘College Words and Phrases’ in DN II:i 31: crust, n. Forwardness.
1901		Bulletin (Sydney) 23 Nov. 20/2: The Bulletin, wearied by half-baked, doughy Tories, with no crust on them, welcomes with joy any utterance from the genuine article like Henry Scotland.
1908		B. Fisher A. Mutt in Blackbeard Compilation (1977) 73: You’ve got a crust to speak to me without an introduction.
1914		M. Glass Abe And Mawruss 131: ‘Schnorrer! Cripple! With my money yet!’ and ‘Crust that feller got it!’.
1922		E. Pound letter 9 July in Paige (1971) 180: Having the crust to attempt a poem in 100 or 120 cantos long after all mankind has been commanded never again to attempt a poem of any length, I have to stagger as I can.
1932		E.S. Gardner ‘Bird in the Hand’ in Goulart (1967) 271: ‘The crust of the damned fool!’ he exploded.
1945		A.J. Liebling ‘Quest for Mollie’ in Just Enough Liebling (2004) 174: She [...] said he had always had an awful crust.
1953		R. Chandler Long Good-Bye 64: ‘After Allbright talked to Gregorius?’ ‘No. Not after that.’ He nodded shortly. ‘You got a crust asking Allbright to use ammunition on that slob.’.
1960		R.M. Rogers Long White Cloud 171: Of all the crust – the Grand National. His race.
1971		Wodehouse Much Obliged, Jeeves 156: Fat slobs of dubious parentage who had the immortal crust to send her butler on errands.
1996		H. Roth From Bondage 103: Ira had to admire the kid’s crust, speaking in such tones to Ida.
2005		E. Weiner Big Boat to Bye-Bye 232: ‘Where do you get the crust, angel. Where do you come off saying I’m bad’.