Remove the yolks from the whites and place the yolks in a medium bowl. Carefully clean the whites and set aside.
Add the avocado, mustard, lemon juice, salt and pepper to the yolks and whisk until smooth. Transfer the mixture to a zip top bag and snip off the end. Fill the egg whites with the avocado mixture and set aside.
Cut the olives in half and stuff the end with the large hole with a strip of pepper. Place one olive half on top of the avocado mixture of each egg and then place a few strips of pepper on the white part of the egg to make bloodshot eyes.