Place eggs in a saucepan large enough to hold them all in one layer.
Cover with water.
Bring to boil, then lower heat to a simmer and cook for 9 minutes.
Fill a large bowl halfway with ice and water.
When eggs have cooked, transfer them with a slotted spoon to ice bath.
Let cool completely.
Peel eggs; cut each in half lengthwise.
Remove yolks and place in a bowl.
Mash yolks with a fork until smooth.
Add mayonnaise, mustard, salt and pepper and mix until blended.
Transfer yolk mixture to a piping bag fitted with a plain or star tip, or to a ziplock bag.
If using ziplock bag, seal bag and snip off one corner.
Pipe yolk mixture into empty egg whites.