In a pot or deep skillet, combine about 1 quart water, 1 tablespoon white vinegar and 1 1/2 teaspoons salt. You can poach one to four eggs at a time in this liquid; work in batches for more. Eggs can be at room temperature or refrigerator-cold; cold eggs will require a slightly longer cooking time.
Bring water to a bare simmer (the French call it a “smile”), with bubbles forming on the bottom of the pan and only slight activity on the top. The water will be under 190 degrees; you should be able to quickly dip your fingertip in and out without pain.
If you are a confident cook, crack each egg on the side of the pan and let the contents slide very gently into the water. If you need to worry about broken yolks or bits of shell, break each egg into a separate ramekin before you begin to cook. Hold the ramekin just above the water and turn it over quickly but gently, to keep the whites and yolks close together.
Let cook until just firm, 4 to 5 minutes. The yolks will be soft and plump and the whites will be set but not tough. Use a slotted spoon to lift eggs out one at a time. Let drain on a clean kitchen towel or paper towels. Use the edge of the spoon or a small knife to trim off any ragged edges.
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