My electric kettle switches off completely when the water was boiling one time. So you have to restart it, if you forget the hot water.

But the egg-cooker has a very clever solution to achieve the same as your device. Unfortunately it could be considered as not-a-hack as it does NOT include a microcontroller, no Raspberry Pi, not even an Arduino :-)

A beeper is connected in parallel to the thermostatic switch. Probably with some capacitive dropper supply, so it works at 230V. So as soon as the switch opens because the eggs are finished (all water evaporated, temperature rises above boiling point of water) the beeper activates, its current flowing through the element. Of course the current of  the beeper is much less than the current the heating element uses, probably just some milli-Amps. Therefore the resistance (around 150 Ohms for 360W @ 230V) of the element is negligible in the circuit, once the beeper works. In fact it is just a good inrush current limitation for the capacitve dropper circuit.

Determining from the strange modulated sound of the beeper, they did not even include an electrolytic for smoothing.