Place eggs in saucepan with water to cover and bring to a boil. Add a tsp. of vinegar and pinch of salt. This helps contain egg whites from leaking out of any cracked shells.
Reduce heat to low once it starts boiling. Cook for 15 minutes.
Remove from heat. Cover and let it sit for 20 minutes.
Pour off hot water and refill pot with cold water. Let them sit in cold water for 5 minutes.
Crack the eggs while cooling by rolling each egg on a hard surface. Carefully peel of the shell.
Slice eggs in half, lengthwise. Gently remove yolk halves and place in bowl.
Mash with fork and add mayonnaise, mustard, and relish.
Place egg white halves on a serving platter.
Scoop spoonful on yolk mixture into each egg white half. Sprinkle with paprika.
Notes
I always use about 8 but boil more just in case the shapes look weird on some.