Place eggs in a pot large enough to hold them all in a single layer. Cover by 3 inches of cold water and place on the stovetop over high heat. Once the water starts simmering briskly, reduce heat to medium high and cook for 12 minutes. Use a slotted spoon to transfer eggs to a bowl of ice-cold water. Let cool for 5 or 10 minutes, then peel. Slice eggs lengthwise. Remove yolks and place them in a medium bowl. Arrange egg white halves on a rimmed baking sheet.
To prepare the filling, add parsley, capers, anchovy paste, lemon zest and juice, mayonnaise, mustard and water to yolks and mash. Taste and add pepper. The filling will be salty from the capers and anchovy, so additional salt will not be needed.
Use two small spoons to scoop filling into egg white halves. Sprinkle with chopped parsley and serve.
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