This is brainless, and the result is a spectacular dinner-party trick. Get your water bath to 165C, then carefully lower in extra-large (55g) eggs (in their shells, of course), at fridge temperature.
Cook 13 minutes, remove. Is all. Adjust the time slightly for smaller eggs, or if you want them more or less runny.
Either hold them at 135F until ready to serve, or immediately chill in ice-water, draw a "P" on the shell prominently, and put them back in their carton. To extend fridge life to over a week, lightly coat with oil or butter. Before serving, bathe them back to 125F for as long as you feel necessary.
For the party trick: (Say) serve a frisee salad with lardons to your guests, then walk around cracking "raw" eggs and opening them above the salads. The first one will elicit horrified gasps, followed by giggles for the others.
Notes: The recipe as-given pasteurizes the eggs. If you like them more rare, and are worried about salmonella, bathing them at 135F for a while will reliably pasteurize them without degrading them much.