Fill a medium saucepan with 3–4 inches of water and bring to a gentle simmer. Add vinegar. Crack one egg into a fine-mesh strainer placed over a bowl and let sit for 10–15 seconds to drain thin whites. Transfer egg to a small bowl. Create a gentle swirl in the simmering water and carefully slide the egg into the center. Cook for 3–4 minutes until whites are set and yolk remains soft. Remove with a slotted spoon and place on paper towels. Repeat with remaining eggs.
Notes
Keep water at a gentle simmer, not a boil. Use fresh eggs for best results. The strainer step removes thin whites for cleaner shape.