What is the name of the cooking method of the eggs in the picture?
A poached egg is an egg that has been cooked, outside the shell, by poaching. it is dropped from its shell and cooked in simmering water for about five minutes.
The egg is cracked into a cup or bowl of any size, and then gently slid into a pan of water at approximately 75° C (167 °F) and cooked until the egg white has mostly solidified, but the yolk remains soft. The "perfect" poached egg has a runny yolk, with a hardening crust and no raw white remaining. In countries that mandate universal salmonella vaccination for hens, eating eggs with a runny yolk is deemed safe for consumption. Broken into water at the poaching temperature, the white will cling to the yolk, resulting in cooked egg white and runny yolk.
Fresh eggs have tight “jelly-like” whites so you can literally crack them into hot water and you’ll pull out a perfect poached egg, no tricks required.
In old eggs (~3 days+), the egg whites begin to break down and become increasingly watery which is what creates the frustrating white wisps that cloud your water and ruin the look of your finished egg.