Prepare Ice Bath: Fill a large mixing bowl with ice water and set aside.

Boil Eggs: Bring water to a boil in a medium saucepan. Gently add eggs and cook for 7 minutes for medium soft-boiled or 10 minutes for hard-boiled.

Chill Eggs: Transfer cooked eggs to the ice bath for 2 minutes to cool, then peel them while still lukewarm.

Make Egg Salad: In a mixing bowl, mash peeled eggs and stir in sugar, salt, pepper, and mayonnaise (add milk if using). Mix until smooth.

Assemble Sandwiches: Spread butter on one side of each slice of bread. Spoon egg salad onto one slice, top with the second slice, buttered side down.

Serve: Optionally trim the crusts and cut sandwiches in half. Enjoy immediately or store in the fridge for up to 2 days.