Peel the eggshells from eggs and separate yolks and whites. Place yolks in a medium bowl and add sugar, salt and pepper. Mash using the back of a fork until broken down and a few chunks remain; set aside. Finely chop egg whites and set aside.
Add mayonnaise to the mashed yolks in bowl. Stir until mixture is combined and some chunks remain.
Add the chopped egg whites and cream to the yolks mixture. Gently fold until fully combined. Chill for 1 hour for best results.
Spread butter evenly over one side of each bread slice, spoon on the egg salad mixture and make the sandwich. (Traditionally, you would trim off the crust and cut sandwich in half diagonally so you have two triangles.)