Place the eggs in a pan of water then bring to the boil.
As soon as it boils, cover the pan with a lid and turn off the heat. Let it rest for 7 minutes, then drain and rinse the eggs under cold water. Leave the eggs in a pan of cold water for 15 minutes to cool completely.
Meanwhile, finely chop the anchovies and dill.
To crack the shell of the eggs, put them in a bottle-shaped container (one by one) and shake until the shell loosens, then peel the bits off with your fingers.
Rinse the eggs, then cut them in half lengthwise. Spoon out the yolk into a bowl and mash with a fork. Stir in the mayo or crème fraîche and mustard, then combine well. Add plenty of freshly ground pepper, then mix well. Taste and adjust it to your liking (you can add a pinch of paprika or cayenne if liked). Add a pinch of salt, if needed.
Fill the egg whites with the mixture and place them on a serving plate.
Chill until serving.
Garnish them with chopped dill just before serving.