To hard-boil the eggs, fill a pot with water and bring it to a boil. Insert eggs and boil for 12 minutes. Remove from heat and run under cold water and let cool, then peel.
Once peeled, cut eggs in half lengthwise and scoop out egg yolk and place in a bowl.
Mash cooked yolks with a fork, and then add mayonnaise, mustard, vinegar and salt, mix with a whisk. Keep mixing until lumps are gone.
Pipe or spoon egg yolk mixture into the egg cups. Piping is easy by filling a plastic bag with yolks and snipping the corner. Fill each egg white with enough filling to mound over the top a bit. Sprinkle with paprika.
Cover lightly with plastic wrap and refrigerate for up to one day before serving.
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Notes
An alternate method to hard-boil eggs is to cover the eggs with water in a pot, bring the water to a boil, and then let the eggs sit off the heat for about 10 minutes.Eggs can be hard-boiled the day before the recipe is made.