Carefully place the eggs in a pot large enough to hold them comfortably in a single layer. Fill the pot with cold tap water, covering the eggs by an inch. Bring the eggs to a boil over high heat. As soon as the eggs begin to boil, turn the heat to low, cover the pot, and time 14 minutes.
When the timer goes off, quickly drain the eggs. Shake the eggs briskly in the empty pot to crack them all over. Run cold tap water over them until the water the eggs are sitting in is cool. Carefully peel the eggs. You may find they peel easiest under the water, or with cold water running over them.
Slice the eggs in half and put the yolks in a bowl, reserving the whites. Add salt and pepper to taste and mash the yolks with a fork. Fold in the pickle relish, mayonnaise, and mustard, combining well.
Using the fork, fill the whites generously with the yolk mixture. You will probably have a couple of extra whites, and that's okay. Dust with paprika and serve chilled.
