3 tablespoons mayonnaise, salad dressing or half-and-half
1 teaspoon yellow, Dijon or spicy brown mustard
⅛ teaspoon pepper
Place eggs in single layer in 2-quart saucepan. Cover with cold water at least 1 inch above eggs. Cover saucepan; heat to boiling.
Immediately remove from heat; let stand covered 15 minutes (12 minutes for medium and 18 minutes for extra-large).
Drain. Immediately place eggs in cold water with ice cubes or run cold water over eggs until completely cooled.
To peel, gently tap egg on countertop until entire shell is finely cracked. Roll gently between hand to loosen shell. Starting at large end, peel egg under cold running water to help remove shell.
Cut lengthwise in half. Slip out yolks into small bowl; mash with fork. To prevent eggs from tipping on the serving plate, cut a thin slice from the bottom of each egg white half before filling. Or, to stand eggs upright, cut crosswise slice about 2/3 from top of narrow end of egg to remove yolk; cut thin slice from bottom of wide end of egg white to rest on serving platter.
Stir mayonnaise, mustard and pepper into yolks. Fill whites with egg yolk mixture, heaping it lightly. Cover and refrigerate up to 24 hours.
Buy eggs 7 to 10 days ahead of time for easier peeling. This gives eggs time to take in air, which helps separate the membranes from the shell.
Heat just to boiling to prevent eggs from cracking. If left to boil, the bubbles toss the eggs around in the pan, which can cause their shells to crack.
For the easiest peeling, peel hard-cooked eggs as soon as they are cool enough to handle.