.... mix cigar or cigarette ashes with butter to make a paste; use the paste
to clean the cabinet.

Just a shot in the dark here, but isn't that basically the recipe for
lye soap?

Robert Bunsen, the great chemist, smoked a lot of cigars. When Kirchoff and Bunsen were working with their spectroscope, they discovered an unusually high amount of potassium levels in their lab. It was from Bunsen's cigar ashes.

Butterfat is a mixture of triglycerides, which will undergo saponification with an alkali. So it's possible that a small amount of a potash soap could result.

Any chemists care to comment?

I'm not a chemist, and I don't play one on TV.