Fill a saucepan with cold water and place over medium heat; stir in vinegar and salt. Bring to a gentle, slow simmer and reduce heat to low.
Break each egg into a separate small ramekin; place a ramekin close to the surface of the water and gently pour egg into the simmering water. Let egg white set for a minute or two and use a silicone spatula to gently lift egg from the bottom of the pan to prevent sticking. Cook until white is firm and yolk is runny, about 6 minutes.
Lift poached egg from water using a slotted spoon and transfer gently to bowl of ice water to stop the cooking process. Reheat eggs for 1 1/2 to 2 minutes in very gently simmering water and remove with a slotted spoon. Tap bottom of slotted spoon containing egg on a dry paper towel to remove any excess water before serving.