Normally I, start with cold water in salted water, It keep the shells firm...then simmer our XL eggs for 20 minutes..we are just about 4000' The yolks are done and whites set, never rubbery.
I have a similar strategy to Chef June and pierino. Cover the eggs in plain water (especially for the Momofuku eggs which bathe in a very salty marinade, I wouldn't pre-salt them), bring to a very gentle boil and boil for one minute, then remove from the heat and cover for 6 minutes (longer if you are at significant altitude). This timing results in firm (not rubbery) whites and moist but firm yolks, kind of the texture of soft peanut butter.
First off, you don't want to BOIL them. My whole life, I've put cold eggs into a cold pan and covered them with cold water. Add about 2 tsps Kosher salt. Place over a medium fire and bring the water to a boil. When the water is boiling, turn off the heat, cover the pan and let the eggs sit for 20 minutes. Then put the pan in the sink and run cold water into the pan until the water in the pan is cold to the touch. You should have perfectly hard-cooked eggs.
I've pretty much always done this type of technique except for the salt- put the eggs in a pan in cold water and bring to a boil, let boil a minute or two and then cover and remove from heat..... Since the directions for the soft ones were so specific in minutes and seconds, I thought there might be a secret time I didn't know about. :)
I steam my eggs in a vegetable steamer. They turn out perfectly every time. I let mine go for 11 minutes which leaves the yolk cooked through, but still a little moist and creamy. Maybe you would want to go twelve minutes if you go the steaming route. I think I got the technique from Serious Eats.
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