Fill a deep, wide skillet with enough salted water to reach a depth of 2 inches. Bring to a gentle simmer over medium heat. Crack 1 egg into a small bowl, then slip into the simmering water; let cook until barely translucent. Using a slotted spoon, gently gather the egg into the center of the skillet and cook until the yolk feels like a water balloon when lifted out of the water, about 3 minutes. Transfer to a damp kitchen towel and repeat with the remaining eggs.
Trim the egg white of any ragged edges, if desired. Serve immediately. (If not serving the eggs immediately, place the poached eggs in an ice-water-filled bowl for up to 30 minutes. Reheat in simmering water for 30 seconds before serving).