I was lucky to find a near perfect recipe. I was able to make a perfect poached egg easily the first time around. I am pleased. Also, I've provided additional detailed instructions in this Food Nirvana recipe to make it pretty much foolproof.
It is necessary to use a fine mesh sieve to allow any runny egg white to flow through it and be discarded. Otherwise the runny part will separate from the rest of the egg during cooking and form useless wads/strings of cooked egg white in the boiling water.
Here are the caveats: 1) The fine mesh sieve, if it is too fine, will not let runny egg white through it, so that defeats the purpose of using that particular fine mesh sieve. Find one with slightly larger grid openings. 2) A jumbo egg and an extra large egg require more cooking time than a large egg, so allow 3 minutes for a large egg, 3 1/4 minutes for an extra large egg, and 3 1/2 minutes for a jumbo egg.
If you are making only one egg then use the stirring step described below to create a vortex in the water before adding the egg. If you are making multiple eggs at the same time do not create the vortex. Also, initially process each egg in the sieve individually and then put each egg into a separate rameken or small bowl.
Ingredients:
One fresh large, extra large or jumbo egg (or more than one egg [maximum four], but all of the same size)
1 tbsp. of white or cider vinegar
A large (8" or more in diameter) saucepan with boiling water 4" deep
Other kitchen stuff:
A ramekin large enough to hold a raw egg.
A fine (but not too fine) mesh sieve.
A somewhat large serving spoon for stirring the lightly boiling water in a saucepan into a vortex.
A large slotted spoon for removing a poached egg from lightly boiling water. Also for removing any unwanted cooked runny egg white.
A kitchen timer
Directions:
Bring a large saucepan with water 4" deep to a boil on high heat, then reduce the heat to low.
Crack the egg into a fine mesh sieve (over a small bowl) and discard the runny egg white (if any) that drips into the bowl.
Carefully transfer/pour the egg into a small ramekin or small bowl. You don't want the yolk to break.
Add one tablespoon of light-colored vinegar to the boiling water in the saucepan and stir the water to create a vortex.
Pour the egg from the ramekin carefully into the middle of the vortex and set a timer for 3 minutes for a large egg, 3 1/4 minutes for an extra large egg, or 3 1/2 minutes for a jumbo egg.
After a minute or two, use a slotted spoon to remove and discard any cooked egg white that is not part of the main body of the egg. It is the stuff that is floating above the egg.
Once the egg is done cooking, use the slotted spoon to remove the poached egg from the water, let water drain from the egg for a few seconds, then put it into a small bowl.
Dab any water from the inside of the bowl and from the surface of the egg, with a folded paper towel, then use/serve the egg.
Enjoy!