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To reduce the potential for cracking during cooking, use eggs at room temperature.
Put the eggs in a saucepan in just one layer. Add cold water to cover them by at least 2 cm. Add a pinch of salt or one tablespoon vinegar to limit damage in case the egg cracks (the egg white will then coagulate right away on the shell sealing the crack rather than spreading into the water).
Bring to a low boil, lower the heat, and cover. Start measuring the time: 3 min for soft-boiled and 10 min for hard-boiled egg.
When ready, remove from heat immediately and cool down rapidly in cold running water to stop the cooking and prevent a green circle from forming around the yolk. This quick cooling makes the peeling easier. To peel, tap the egg against a hard surface to crack shell, then begin peeling from the air-pocket (wider) end. The shell should come off in spiral strips attached to a thin membrane.
To reduce the risk of breaking, always use 100% fresh eggs and allow them to reach room temperature before poaching.
Use a medium-size skillet or saucepan (about 25 cm diameter). Fill it with water to a depth of about 7 cm and put it on high heat to bring it to a boil. In the meantime, crack each egg into separate small cups or bowls. When the water in the skillet starts boiling, add one tablespoon of plain vinegar and some salt. Vinegar helps the egg to hold its shape.
With the water just barely simmering, gently lower the lip of each egg-cup 1 cm below the surface of the water and let the egg flow out. Immediately cover the skillet and turn off the heat. Cook the eggs 3 min for medium-firm yolks, adjusting the time up or down for firmer or runnier yolks. Lift each perfectly poached egg from the water with a slotted spoon, but hold it over the skillet briefly or place it on a towel to let any water clinging to the egg drain off.
In order to better control the poaching, avoid doing batches larger than 4 eggs at a time. To poach more than 4 eggs, use more than 1 medium-size skillet or work in subsequent batches. After poaching, eggs may be placed in a bowl of warm water and kept warm prior to serving while making new batches.
Poached eggs may also be prepared in advance. After poaching, put them in a big bowl of cold water, to stop the cooking, then keep them in the refrigerator up to 3 days. When ready to eat, fill a pan with water to a depth of 2 cm and heat until it simmers. Drop the eggs in, using a slotted spoon, and heat them about 30 sec to 1 min, just to warm them through.