Add at least 3 inches of water to a large skillet over medium high heat. Bring the water close to a boil, where small bubbles have formed and are rising to the surface and popping (about 200°F, if you really want to measure). Add 1 tablespoon of vinegar to the pan and mix in.
Crack an egg into a fine mesh strainer to remove the more watery portion of the whites. Transfer egg to a small bowl. Remove pan from the heat.
Gently tip the eggs into the hot water, one at a time, leaving enough room between the eggs that the whites don't touch. You can add 4 to 6 eggs, depending on the size of your pan, making sure to leave room between eggs.
Place lid on the pan and set the timer for 3 minutes and 30 seconds for large eggs.
Using a slotted spoon, remove eggs from the water in the order that you added them to the water. Test for doneness by gently poking the white. If you want them more cooked, dip them back in for 15 to 30 seconds.
After removing eggs from the pan, place your egg on a towel for a couple of seconds, to remove excess water, then transfer to your plate.