Eggs: In a large saucepan or deep skillet, heat 2–3 inches of water, vinegar, and 1/8 teaspoon of salt to boiling; adjust heat to keep liquid simmering gently. Break eggs into a small bowl, one at a time.
Hold bowl close to surface of pan and slip eggs into water.
Cook eggs until whites are completely set and yolks begin to thicken, but are not hard (approx. 3–5 minutes), do not stir.
Lift eggs from water with slotted spoon; drain well on a platter lined with paper towels. Keep warm.