Boil the eggs for 14 minutes. When done, transfer to a bowl with ice water to stop it from cooking any further. Peel the eggs under cold running water, then cut them in half lengthwise. Remove the yolks using a small spoon. Put the yolks in a small bowl and the egg whites on a serving platter. Take a fork and mash the yolks in the bowl.
Add mayonnaise, Dijon mustard, apple cider vinegar, and salt and pepper to the crumbled yolks. Mix well.
You can use a plastic freezer bag, as mentioned above, to fill the egg whites with the yolk mixture, or you can use a teaspoon to fill them up. If using a bag, fill a corner of it with the egg yolk mixture, puncture the tip of the corner slightly, then squeeze the mixture through it into the egg whites.