Pretty much what I’ve always done. I bring the water to a boil, and then turn it down to simmer. Five minutes for soft-boiled eggs, ten minutes for hard. No need for ice water, just cook them ahead of time and let them cool.
I don’t believe in wasting fuel. Once you bring water to a boil, it’s not going to get any hotter than 212 degrees, so what’s the purpose in keeping the gas turned up? Waste of money, unless you’re cooking something where the water has to be boiled away.
I just put the eggs in the pot with tap water, bring to a boil, remove from heat immediately, allow to cool. Voila, perfect soft boiled eggs.