Put as many medium eggs as you need in a saucepan to fit in a single layer and generously cover with cold water. Place the pan over a medium heat and bring to a full rolling boil. Set a timer and cook the eggs for exactly 6 minutes; the yolks will be set but not overcooked.
Put a large bowl in the sink and use a slotted spoon to transfer the eggs to the bowl. Let cold water run over the eggs as you use the back of the spoon to gently smash the shell of each one in several places, then add a few handfuls of ice cubes and enough water to cover the eggs.
Peel, then rinse each egg under running water and return to the bowl of ice. Once fully cold, place the eggs in a bowl, cover it with clingfilm and refrigerate until needed.