I learnt (from Nursery Rhyme books, not hearing it) Pease PUDDING hot...
I think it may be like mushy peas, cooked till solid. In the days before freezers and canning, dried peas, soked overnight would have been a poor man's staple (but even without the oatmeal, probably ugh)

I meant to write Cinderella Rockafella, which I've seen here as the rhyme you quoted. I assume it comes from the Pop song that I heard in April 1968 but don't remember (I know where I was living when I heard it, not much else)
You're the lady
You're the who
rocks me
You're the fella
You're my rockafella

I don't listen to pop songs much but was living in a YWCA, while flat-hunting and couldn't escape it.
You're my Cinderella

It was sung by 2 people and is all mixed up in my memory and probably wrong.