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