Method:
Fill a saucepan with enough water to generously cover the eggs, bring to a boil and reduce to a simmer.
Using a slotted spoon, gently place the refrigerator-temperature eggs in the simmering water and start timing.
Prepare an bowl of ice-water
After exactly 6 minutes, remove with the slotted spoon and transfer to the ice-water for 60 seconds. Serve.
Notes:
The problem with soft boiled eggs is that you want to get the white set, and the yolk runny; whilst getting consistent results. Looking at the table below, you can see that we want the yolk around 145, but the white at 158.
Despite all the assertions of "the perfect egg" sous-vide, this seems like an inappropriate technique for soft-boiled eggs - it's going to get you a homogeneous temperature, the yolks will be overdone by the time the whites are set.
Others have suggested heating the eggs starting in cold water, or starting in boiling water and turning off the heat. Unfortunately, neither of these can produce consistent results, it varies by the pan shape, the amount of water and the number of eggs. In order to get consistency we must hold the water at as close to boiling point as we can get - a simmer.
Few people are going to have the patience or planning to start eggs from room temperature, and the colder temperature gives a higher difference from the boiling water, making it easier to achieve the temperature gap between the yolk and white as we cook.