In a dry manner; with little emotion or without enthusiasm; sarcastically or matter-of-factly.
From 'dry' (Old English 'dryge') plus the adverbial suffix '-ly' (Old English '-lice'). The metaphorical use developed from physical dryness to emotional coldness or lack of sentiment.
Drily delivered humor is actually harder to write than jokes with punchlines—think of how British comedians master deadpan delivery—because the audience has to recognize the wit themselves, which makes it feel more clever and sophisticated.
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