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.