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