In a saucepan, arrange the eggs in a single layer and add water until there are 1 1/2 inches of water above the eggs.
As the water starts to boil, turn the heat down to low, cover the pan, and cook it for 1 minute.
Remove from heat and cover for 15 minutes; then, repeatedly rinse with cold water for 2 minutes.
Crack egg shells, peel them carefully under cool running water, and pat them dry with paper towels.
Cut the eggs in half lengthwise, transferring the yolks to a mixing bowl and the whites to a serving platter.
Using the back of a fork, mash the yolks into a fine crumble. Add mayonnaise, pickle relish, black pepper, and salt, and mix well.
Put a portion of the deviled egg mixture back into each egg white hole using a spoon.
Sprinkle paprika or black pepper on top as garnish.