Puncture the large end of each egg with a straight pin or ice pick to release the air from the egg and make a perfectly shaped cooked egg.
Place eggs in a medium size sauce pan and cover with lukewarm tap water. (If you are going to color the eggs for Easter, add about 1 tablespoon of white vinegar.)
Cover pan and bring water to a gentle rolling boil. Turn off heat immediately, leave pan covered and set timer for 15 minutes.
At the end of the time carefully drain hot water from pan and fill pan with cold tap water and a dozen ice cubes. This prevents over cooking as well as making the shells easier to remove. Let sit for about 15 minutes, drain water.
Chill eggs until ready to prepare. Remove shells and rinse.
Deviled Eggs
Cut eggs lengthwise in half. Carefully remove yolks to a small bowl. Mash yolks thoroughly with a fork. Add mayonnaise, ground mustard, salt and pepper.
Spoon mixture evenly into egg whites. (If you are so inclined, you can fill a pastry tube with the yolks to fill the whites for a fancy presentation. A heavy plastic storage bag can be substituted for a pastry tube. Spoon the filling into the bag, push into one corner and snip off about a quarter inch of the tip.)