Fill a large saucepan with 2 to 3 inches of water and bring to a boil. Reduce heat to medium-low, pour in vinegar, and keep the water at a gentle simmer. Crack an egg into a small bowl then gently slip egg into the simmering water, holding the bowl just above the surface of water. Repeat with the remaining eggs. Cook eggs until the whites are firm and the yolks have thickened but are not hard, 2 1/2 to 3 minutes. Remove the eggs from the water with a slotted spoon, dab on a kitchen towel to remove excess water, and place onto a warm plate