Eureka! I made it! I had never managed to poach an egg without destroying it! But I found the magic method! Simply follow these steps.
1) Bring water to the boil
Super trick number 1: add a spoon of white vinegar in the water (supertrick number 1 bis: of course I don’t have white vinegar in my kitchen so I used balsamic vinegar, it doesn’t change anything except maybe for a slight taint of the egg)
2) The egg has to be super fresh (if you use the egg that has been in your fridge for 2 weeks, it might not work so well)
Supertrick number 2: don’t break the egg directly in the pan, put it in a bowl or cup first
3) Before putting the egg in the water, reduce heat: the water must not be boiling with bubbles
SuperSuper trick number 3: form a vortex in your pan: with a wooden spoon, turn the water until a vortex appears.
Then, put your egg gently in the middle and wait.
Let cook between 2 and 3 minutes according to size, no longer if you want to keep the yolk soft!
4) When cooked remove the egg from the water and place on absorbant paper