You might not think of sous-vide as the perfect cooking method for cooking eggs, but think again. J. Kenji Lopez-Alt over at Serious Eats shows us that if you can control the temperature of your water, all you need is time to end up with deliciously poached, soft-boiled or hard-boiled eggs, all in the shell.
Kenji walks us through the times and temperatures required for poached eggs are different consistencies, but settles on water that's about 75 degrees C (167F) for 13 minutes. The end result is an egg you can peel like a normal boiled egg (only the top, since you'll essentially dump the poached egg out from the top) but has a creamy poached consistency to it:
By cooking eggs for 13 minutes at 167°F, you eliminate the need for the seconds-accurate timing you'd need with boiling or simmering water.
The slightly higher temperature also builds in a temperature gradient — the whites get hotter than the yolks. Thus you end up with an egg with a yolk that is just barely beginning to thicken and a white that is relatively firm. With this method, the thin white will not thicken completely and will drop away easily from firm tight white.
He also explains a 45-minute method at a lower temperature, around 63 degrees C that yields a much softer egg that can then goes into simmering water for just a minute for an absolutely perfect poach. If you prefer soft-boiled, he has another method that gets just the right consistency but also makes them easy to peel. The post also walks you through a number of temperatures to show you how quickly the consistency of an egg can change — that way you can pick the one that looks best to you.
The beauty of this method is that you don't have to do too much to get the texture you're looking for. Bring your water up to the right temperature, try to keep it there (within a few degrees), and then start the timer. If you're using a large enough volume of water, it'll retain its temperature long enough for you to cook your eggs to the perfect consistency. Hit the link below to dive into the science of soft-boiled eggs.
The Food Lab's Guide to Slow-Cooked, Sous-Vide-Style Eggs [Serious Eats]