Bring 1 inch of water to a boil in a saucepan fitted with a steamer basket. Add eggs, cover and steam for 13 minutes, then move immediately to ice water for 10 minutes.
Peel the cooled eggs and chop into small pieces with a knife. Fold in crème fraîche, Dijon, dill, lemon juice, salt and pepper without beating the eggs smooth.
Cover and refrigerate the salad for 20 minutes. Spread a thin layer of softened butter over one face of all 16 bread slices.
Divide the salad equally among eight buttered slices and spread into a level layer almost to the edges. Close with the remaining bread, buttered faces inward.
Trim crusts with a sharp serrated knife and cut each sandwich into three fingers. Keep the 24 pieces refrigerated in a covered container; allow two fingers per serving and use within 24 hours.