The Vortex Method
This method requires a little skill but once you get the hang of it, it’s super easy to do! You’ll have just a small amount of whites hanging off and you can easily cut them away to serve.
Select a wide pot and set some water to boil then simmer. Crack the egg into a small cup (a 1/3-cup measuring cup works well). Use a spoon to swirl the water around for about 15 seconds as you try to create a hole or vortex in the center. The swirling current will help to wrap those fly-away whites around the yolk.
As you remove the spoon with one hand, gently pour the egg into the vortex with the other hand. Poach for a few minutes and remove. Mastering this method will take trial-and-error but you’ll be so proud of yourself once you get it down pat!
You could combine Method 5 with Method 4 to get rid of the watery part of the egg white first before adding to the vortex as it's the watery part of the egg white that creates much of the wispy white mess.