Boil the Eggs Properly: Place the eggs in a saucepan and cover with cold water. Bring to a gentle boil, then reduce heat and cook for 9–10 minutes. Transfer immediately to cold water to stop cooking and ease peeling.
Peel and Separate: Peel the eggs once cool. Slice in half and separate yolks from whites, keeping them in separate bowls.
Create the Creamy Base: Mash the yolks with a fork until smooth and fluffy. Add mayonnaise, sugar, salt, and pepper, mixing into a creamy paste. Optionally, add a splash of milk or cream for softness.
Chop and Combine: Finely chop the egg whites into small pieces. Gently fold them into the yolk mixture until cohesive and spreadable.
Prepare the Bread: Spread a thin layer of butter on each slice of bread to prevent sogginess.
Assemble the Sandwich: Spread the egg mixture evenly on one slice, top with another slice, press gently, trim crusts, and slice into halves or rectangles.