Place the eggs in a medium saucepan with cold water to just over them.  Heat the pan over medium high heat.  When the water comes to a boil, turn it off and cover the pan.  Let the eggs rest for 14 minutes then immediately plunge them into a bowl of ice water.  The eggs should rest in the ice water for at least 5 minutes, or until cool.

When the eggs are cool, peel them, cut them in half lengthwise, and carefully scoop the yolks into a medium mixing bowl.  Place the whites, cut side up, on a serving plate.  Use a fork to mash the egg yolks until they are fairly smooth.  Add the mayonnaise, celery, mustard, shallots, 1 teaspoon of the dill, 2 tablespoons of the celery, and the cayenne.  Sprinkle with a pinch each of salt and pepper and stir well.

Using a small spoon, scoop the yolk mixture into the whites.  Alternatively, transfer the yolk mixture to a small plastic bag, cut a ½-inch hole in one corner, and pipe the mixture into the whites.  Top the eggs with a sprinkle of remaining dill and celery.