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 water at a simmer. Crack an egg into a small bowl then gently pour egg into simmering water. Repeat with remaining eggs. Cook eggs until the whites are firm and the yolks have thickened but are not hard, 2 - 3 minutes. Remove eggs from water with a slotted spoon, dab with a paper towel to remove excess water, and set aside on a plate.