Place eggs in a medium saucepan and cover with cold water. Bring water to a boil and immediately remove from heat. Cover and let eggs stand in hot water for 10 to 12 minutes. Remove from hot water
cool
and peel.
Slice eggs in half lengthwise. Remove yolks and place in a medium bowl; set aside egg whites. Use a fork to mash egg yolks with mayonnaise
Dijon-style mustard
salt
and black pepper.
Fill hollowed egg white halves with yolk mixture. Sprinkle with cayenne pepper. Cover and chill in the refrigerator until serving.