Mash eggs: In a bowl, place the boiled eggs and break them apart using a fork. Once they are mostly broken into chunks, use a potato masher to crush the eggs further until you achieve a creamy texture with smaller egg white pieces.
Prepare the filling: Add the mayonnaise, mustard, chives, black pepper, and salt to the mashed eggs. Gently mix everything until well-combined. Taste and adjust the salt if needed—use caution, as eggs require minimal salt.
Assemble the sandwich: Lightly butter the slices of bread. Spread the egg mixture evenly across 4 slices, ensuring the filling reaches all edges. If you prefer, cut the sandwiches as desired (see Note 4 for tips).
Serve: For the best flavor, always serve the sandwiches at room temperature.