"RM" == Ralph Mowery writes:

RM Check for a loose wire somewhere in the circuits that are affected. Check
RM the voltages at the affected devices to see if they change when the frying
RM pan is cut on and off.

Thanks but a ham told me (in Chinese) that this is a well known
phenomenon with cheap current limiters, that take a bite out of each
crest of the AC sine wave as their method of limiting. That's why such
appliances cause power supplies in the same house to hum when such
appliances are switched to LOW or MEDIUM, but not HIGH. If only I
could find the English name of this phenomenon, I could look up what
to do about it.