Fill a small saucepan with water and bring it to a gentle boil. Meanwhile, break the egg into a small bowl. This will make it easier to slide the egg into the hot water while keeping its shape.
When the water has reached a gentle boil, add the vinegar. The vinegar helps the egg white congeal.
Use a hand whisk to vigorously whisk the water, then slide the egg into the whirlpool. This will help the egg hold its shape when it first enters the water. If making more than one egg, repeat the process (use a larger saucepan).
If some of the egg white spreads out and does not curl around the yolk, gently push it in with a spoon.
Cover the pot, turn the heat off, and set the timer for 5 minutes.
After 5 minutes, use a slotted spoon to lift the egg out of the water and place it for a few seconds on a paper towel to drain.
The egg white should be cooked yet creamy, and the yolk should appear soft. When cut open, it should be thick but gooey. Season the egg with salt and pepper, and enjoy!
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Notes
The vinegar helps the egg whites congeal. The faster the egg whites cook, the less risk the whole egg will disperse in the water, leaving you with an unappetizing boiled scramble.
You add just a small amount of vinegar, so you don't actually taste it. Regardless, using mild-tasting vinegar, such as rice or champagne vinegar, is a good idea. Having said that, I've used plain white vinegar plenty of times, and it was just fine.
Five minutes should produce runny but jammy and thick yolks. That's exactly how I like them. If you like runnier yolks, keep the eggs in the hot water for just four minutes.
When you serve the eggs on any type of bread, make sure to drain them for a few seconds on a paper towel to prevent soggy bread.
While you can find tips online for storing and reheating poached eggs, I don't like storing them. I only make as many as my family will eat right away.