Peel 6 hard-boiled large eggs. Halve each one lengthwise. Scoop the yolks out into a medium bowl.
Mash the yolks with a fork until finely crumbled. Stir in ½ cup mayonnaise, 1 teaspoon Dijon mustard, 1 teaspoon finely grated lemon zest, and ¾ teaspoon kosher salt until creamy.
Chop the egg whites into small pieces. Stir and gently mash the egg whites into the yolk mixture.
Divide the mixture between 4 slices white sandwich bread (about ½ cup each) and spread into an even layer. Close each sandwich with a second slice of bread, then cut each sandwich in half.
