Place the eggs in a large pot and cover with cold water. Bring to a boil over medium heat, then remove from heat and let sit covered for 10 minutes.
Drain the eggs and cool them under cold running water. Peel the shells and slice each egg in half lengthwise.
Scoop the yolks into a mixing bowl. Mash them with a fork until smooth.
Stir in the mayonnaise, Dijon mustard, salt, and black pepper until the mixture is creamy.
Fold the chopped smoked salmon into the yolk mixture until evenly combined.
Spoon or pipe the filling back into the egg white halves.
Top each filled egg with a small dollop of caviar just before serving.