FWIW, I boil my eggs in steam: 5mm-1cm of water in the pot, put the egg in, put the lid on it, heat it up until the water starts boiling, and then turn it off,

FWIW, I boil my eggs in steam: 5mm-1cm of water in the pot, put the egg in, put the lid on it, heat it up until the water starts boiling, and then turn it off, and wait, the steam will continue boiling the egg, and the residual heat will continue producing steam for a while.