Place eggs in a single layer in a saucepan
Add cold water until eggs are covered by about 1 inch
Bring water to a rolling boil over medium-high heat
Turn off the heat
Cover the pan with a lid
Let eggs sit in hot water for 10 to 12 minutes
Transfer eggs to a bowl of ice water
Chill for 5 to 10 minutes
Peel the eggs
Slice eggs in half lengthwise
Remove yolks and place in a bowl
Mash yolks with mayonnaise, mustard, salt, and pepper
Spoon or pipe yolk mixture back into egg whites
Sprinkle with paprika if desired