The best method I've found for peeling shells off hard cooked eggs is to tap their shells all over, against a flat, hard surface to the tune of a TV theme song*. Pinch a small amount of shell off top and bottom of eggs, breaking the thin membrane between the shell and the white, Roll each egg, chubby end up, between your palms, under cold, running tap water to work the water under the membrane. Then use your thumbs to gently slip off the rest of the shell. Repeat for each egg.
Slice eggs in half lengthwise, Remove the yolks to a bowl. Place the whites on a serving dish (I use a black plastic egg server a guest left after bringing store bought egg appetizers from Albertson's.
Mash the Yolks in the bowl with the back of a fork until crumbly.
Add Mayonnaise, Mustard, Turmeric, chopped Shallots, chopped Olives, Salt, and Black Pepper to the mashed Egg Yolks and stir until smooth. Add the tablespoon of Liquid from the Olive Jar to blend the mixture.
Spoon this egg yolk mixture into the Egg White Halves (or use a pastry decorating bag for fancy swirls and peaks).
Sprinkle eggs with Paprika for a devilish look, or with Cayenne Pepper for both a devilish look and taste.
Refrigerate until ready to serve.