Place the eggs in a large saucepan and cover with water by 1-inch. Bring to a boil. As soon as the water comes to a boil, set a timer and boil the eggs for 10 minutes. Remove from the heat and place in the sink. Drain, and run with cold running water until cool enough to handle. Peel the eggs and cut them in half lengthwise.
Remove the yolks from the whites and put them in a medium-size bowl. With the back of a fork, mash the yolks then add the mayonnaise, mustard, lemon juice, Worcestershire sauce, hot sauce, celery leaves and parsley leaves, and mix well. Add the crabmeat and gently stir to mix. Season with salt and lots of freshly ground black pepper.
Spoon equal amounts of the mixture into the egg white halves and chill well before serving.