Place the eggs in a medium saucepan and cover with cold water. Bring to a boil over high heat. Once rapid bubbles start to form, remove the pan from the heat. Let the eggs rest in the water for 15 minutes. Drain and allow to come to room temperature. Once cool enough to touch, remove the shells.
Slice each egg in half lengthwise. Pop out the yolk and transfer to a medium mixing bowl. Add the mayonnaise, mustard, and dill to the yolks and whisk until smooth. Alternatively, you can puree in a food processor. Taste for seasoning and add salt as necessary.
Arrange the egg whites on a work surface and scoop a scant tablespoon of filling into the center of each half. Top with the smoked salmon and garnish with additional dill.