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Oatmeal and milk boiled to a moderate thickness, and eaten with sugar and butter. Figuratively, a wet, muddy road: as, The way through Wandsworth is quite a hasty pudding. To eat hot hasty pudding for a laced hat, or some other prize, is a common feat at wakes and fairs.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Hasty * HatNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes
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Francis Grose was independently wealthy, having inherited money from his father, a jeweller. Finding himself overspending, he published a number of books; his Provincial Glossary seems to have been the starting-point for the Vulgar Tongue reproduced here.