Fill a saucepan with enough water to cover the eggs by 1 inch. Add the salt and bring to a gentle boil. Once the water is boiling, gently lower in the eggs, being careful not to break them. Reduce heat to a gentle boil and cook the eggs 14 minutes. A few minutes before the eggs are finished cooking, fill a large bowl with ice water. With a slotted spoon, carefully remove the eggs from the boiling water and submerge them immediately into the ice water. Let cool completely, about 15 minutes, then peel under cool running water.