Circa 1699 per OED. Figurative extension of the existing meaning.
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I thought it came from the thing you have pictured. But for penis instead of hands. ๐คทโโ๏ธ
a cozy fluffy tube
I think that's your why. As to when, no idea. I first heard people talk about "eating muff" or "muff diving" going back at least 25 years, but I'm sure it's probably much older than that.
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I use ear muffs to protect my ears from cold
edit: and in places it is popular to eat muffaletta

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