Add enough water to come 1 inch up the side of a narrow, deep 2-quart saucier. Add the salt and vinegar and bring to a simmer over medium heat. Meanwhile, crack the egg into a custard cup or small ramekin. Use the handle of a spatula or spoon to quickly stir the water in one direction until it's all smoothly spinning around.
Carefully drop the egg into the center of the whirlpool. The swirling water will help prevent the white from "feathering," or spreading out in the pan.
Turn off the heat, cover the pan, and set your timer for 5 minutes. Don't peek, poke, stir, or accost the egg in any way.
Remove the egg with a slotted spoon and serve immediately. Alternatively, move the egg to an ice bath and refrigerate up to 8 hours. Reheat in warm water just before serving.