Green’s Dictionary of Slang

hasty pudding n.1

[pun; the couple have been ‘hasty’, the child is the ‘pudding’; 1630 citation is double entendre]

a bastard, an illegitimate child.

[UK]Fletcher Chances I ix: Your Brats got out of Alligant and broken Oaths? Your Linsey Woolsey work, your Hasty Puddings?
[UK]J. Taylor ‘Sculler’ in Works (1869) III 30: It is no wonder wherefore little nell, So bigge below the waste begins to swell: For being hungry (in the dark) she stole, / A hastie pudding, and deuour’d it whole.