Place the eggs in a large saucepan; completely cover the eggs 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 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; remove the shells from the eggs; pat the eggs dry; slice in half lengthwise
Remove the egg yolks and place them in a small bowl; mash the egg yolks until crumbled; add the mayonnaise, relish, mustard, and salt; mix until fully combined; spoon the filling into the egg whites
