Green’s Dictionary of Slang

big apple n.1

also apple, apple hat, big apple hat
[? apple-knocker n.; such a hat being similar to those worn by a farm-worker to keep off the sun or f. the size, fig. resembling that of the Big Apple n.]

(orig. US black) a large-brimmed, oversized hat, in 1930s–40s style.

Show quotations
[US]M. Braly On the Yard (2002) 152: Red had attempted to block his rainhat into a style currently in vogue with pimps and hustlers called the Apple.
[US]V.E. Smith Jones Men 7: Decked out from the top of his big apple hat to the tip of his leather platforms.
[US]E. Folb Runnin’ Down Some Lines 109: You have your apple hat on, your flairs, and your boots. [Ibid.] 228: Apple […] Large-brimmed, oversized cap like those worn in the 30s and 40s.