Special equipment: a large mortar and pestle
Mash the anchovies, capers and most of the parsley with a mortar and pestle until a smooth paste forms. Stir in the mayonnaise, olive oil and lemon juice and season with some salt and pepper.
Add the egg yolks and mash until smooth. Mound the yolk mixture in the egg whites, sprinkle with the remaining chopped parsley and serve.