Bring cold, unsalted water to a boil in a sautoir or russe. To help set the whites, add 50 milliliters (about 3½ tablespoons) white vinegar per liter of water (or ¼ cup per quart). Do not add salt to the poaching liquid; it will cause the whites to break.
Set aside a bowl filled with clean, cold water.
When the water comes to a boil, lower the temperature to 82°C (180°F) for poaching.
For quality assurance, break the eggs, one at a time, into a ramekin or small dish. If the eggs are perfect, with unbroken yolks, one at a time, carefully slip the whole eggs into the poaching liquid.
Cook for 3 minutes or until the whites are firm and the yolks are covered with a thin, almost transparent film and remain soft and runny.
Using a slotted spoon, lift the eggs one at a time from the poaching liquid and place them in the reserved bowl of cold water to stop the cooking and remove any trace of the vinegar flavor.
Using a slotted spoon, transfer the eggs to a double layer of paper towels or a clean kitchen towel to drain.
Using a small, sharp knife or kitchen scissors, trim off any ragged edges.
If holding poached eggs for more than a few minutes, refrigerate. Poached eggs may be chilled and held for up to 2 hours. When ready to serve, quickly reheat the poached eggs in simmering, salted water for about two minutes and serve hot as directed in a specific recipe.