Place the eggs in a large saucepan and cover the egg completely with cold water. Place the saucepan over medium-high heat and bring to a boil.
Once the water is boiling, remove the saucepan from the heat and cover. Set aside for 12 minutes.
Using tongs or a spoon, carefully transfer the eggs to a large bowl filled with cold water and ice. Allow to cool in the ice bath for at least 15 minutes.
Remove the eggs from the ice bath, tap the shells on the counter, and carefully peel them off. Run under cold water to remove any small pieces of the shell, pat the eggs dry, then slice in half lengthwise.
Remove the egg yolks and place them in a small bowl. Mash the eggs yolks until crumbly, then add the mayonnaise, relish, mustard, and salt. Mix until fully combined then pipe or spoon the filling into the egg whites.
Sprinkle with paprika and serve or refrigerate until ready to serve.