Put eggs in a large saucepan; cover with water. Cover the pan and bring the eggs to a full rolling boil. Remove from heat and let stand, covered, for 20 minutes.
Add cold water to the eggs to cool and peel.
Cut eggs in half, lengthwise. Remove the yolks to a bowl. Add remaining ingredients to the yolks, with as much mayonnaise as desired for taste and consistency. Mix well. Fill the egg white halves with the yolk mixture and arrange on a platter or egg dish.
If desired, garnish with chopped green onions, chives, or parsley.
Makes 24 stuffed deviled egg halves.