“something resembling the handle of a pan,” 1851, especially in ref.to geography, originally Amer.Eng., 1856, in ref. to West Virginia(Florida, Texas, Idaho, Oklahoma also have them). Meaning “an actof begging” is attested from 1849, perhaps from notion of arm stuckout like a panhandle; verb panhandle “to beg” is from 1903.
Online Etymology Dictionary, © 2010 Douglas Harper
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I have just learnt that “panhandle” is an Americanism for begging. I am fascinated by the beauty of the expression, especially the image of the arm of a sitting beggar stuck out like the handle of a pan. The expression contains an entire word picture of a beggar who sits on a crowded sidewalk extending his begging arm towards the passers by. In India the beggar sticks his hand at you from out of your car window.