Clean pots without scrubbing

I wish I had taken pictures.
It was not a sight for the faint of heart -  my poor little pot suffering from a case of burnt-on pasta, cheese and tomato sauce. A brown, baked on mess. Kind of reminded me of dried blood.
Yep. Pregnant ladies have even worse memories than menopausal ones, so that batch of pasta cooked for about 3 hours.
I tried scrubbing, abrasive cleansers, vinegar and soda. No joy.  As I scrubbed, I was talking to Laura on the phone: I,  cursing this impossible job, she, tending to a teething baby in 35º heat.
"Mom," she said. "Tell me what got burned on. Because if it was rice or pasta, you just boil up some more rice or pasta and it will clean itself."
I threw a handful of pasta into the pot of boiling water and, miracle of miracles, the pot automagically cleaned itself! (That's a pretty smart kid I have.)
Alas, if only I could return the favour with an easy way to soothe a teething baby.