Fill a medium saucepan with water and bring to a boil. While the water heats up, fill a bowl with water and plenty of ice cubes and set aside. Use a spider or slotted spoon to slowly drop the cold eggs into the boiling water. Cook the eggs at a rolling boil for 14 minutes. Drain the eggs and transfer them to the ice water bath. Chill them for 5 minutes then transfer to a towel to dry. Peel the eggs by tapping them on the countertop, then gently roll the egg between the palm of your hand and the countertop to crack the shell all the way around. Peel the eggs under running water.

In a bowl, use a fork to finely mash the eggs. Add the mayonnaise, mustard, and salt, and mash to combine.

If making a sandwich, toast the bread and butter on one side of each slice. Slather a little mayonnaise on one of the buttered bread slices then top it with a layer of lettuce. Top the lettuce with half of the egg salad then the remaining bread slice. Cut in half, and serve.