To make the sauce, mix the herbs, garlic, shallot and anchovies together in a bowl. Stir in the mustard, vinegar or lemon juice and oil and leave, covered, for half an hour or so at room temperature to become what it’s meant to be.
Put the potatoes in cold water with a teaspoon of salt and bring them up to a gentle simmer. Cook them for 14 minutes until tender. It is essential that they are not overcooked, as they must be sliced without falling apart. Cut the potatoes to the width of 5mm while hot (rubber gloves may help to combat finger pain and an occasional wetting of the knife under a hot tap will make the cutting easier).
Combine the sliced potatoes gently with the green sauce, a grinding of black pepper and more salt, if needed, then serve. Alternatively, allow the potatoes to cool and serve the dish at room temperature.