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This is a synonym for an anus which is experiencing problems with producing solid stools (likely due to over-consumption of Yeo Valley yoghurt) and is producing faecal matter that looks more like a melt-in-the-middle chocolate pudding than a healthy poo.

If you were to have sex with a Chocolate Pudding Factory you would end up with your penis looking like a chocolate pudding, hence the name. If you engaged in pegging with a Chocolate Pudding Factory you would likely end up with a Peg 'n' Pud.
"Wow, I think I must have eaten something funny. I have a stomach ache and I've got loads of gas emanating from my chocolate pudding factory!"
via giphy
by Azbo The Great! March 10, 2017
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