Salt water enough to cover eggs. Bring to a hard boil. Turn off burner and let stand for 11 min.
Remove from hot water and put eggs into an ice batch to cool. Then peel and cut in half, removing the yolks.
If some of the whites tear you can put those into the stuffing mix as well. Gently rinse all the "yellow" left from the yolks in the white.
Pulse your hard cooked yolks in a processor, grate on a cheese grater, or use the paddle attachment on your kitchen aid mixer to make a fine mix of yolks.
Put all ingredients (except mayo) into food processor and pulse until smooth.
Mix the tapenade into the mayo. Then fold into your egg mix. You may need to add more lemon juice.
Stuff your eggs and garnish with coarse sea salt and cracked pepper.