Place the eggs in a saucepan, cover with cold water by 1 inch, and bring to a boil over high heat.

Cover, remove from the heat, and let the eggs sit in the hot water for 11 minutes for fully set yolks with no gray ring.

Drain and plunge the eggs into a bowl of ice water for 5 minutes to stop the cooking and loosen the shells.

Peel the eggs and chop them into small, even pieces with an egg slicer or knife.

Fold in the mayonnaise, Dijon, celery, chives, salt and pepper until just combined; the mixture should hold together on a spoon without being wet.

Butter one side of all 16 bread slices, a thin barrier that keeps the filling from soaking in.

Spread about 1/4 cup egg salad over 8 of the buttered slices, all the way to the edges.

Top with the remaining slices, butter side down, and press down lightly.

Trim the crusts with a serrated knife, then cut each sandwich into 3 fingers.

Arrange on a plate, cover and refrigerate for up to 2 hours before serving so the fingers stay neat when picked up.