Place eggs in a 2-qt saucepan. Add enough cold water to cover by an inch. Over medium-high heat, bring to a boil. Once at a rolling boil, remove from heat, cover and let sit for 12 minutes. Strain the water from the saucepan and run cold water over the eggs to cool them. Let the water run over them for a minute or two.
Shake the pan from side to side until there are multiple cracks in each egg. Then carefully peel each egg.
Slice the hardboiled eggs in half lengthwise. Carefully remove the yolks and place into a bowl. Mash the yolks as fine as you can with a fork.
Add the mayo, mustard, vinegar, salt, and pepper and mix until well combined and creamy.
Arrange the whites on a serving platter. Using either two spoons or a pastry bag filled with the mixture and fitted with a decorative tip, evenly distribute the mixture into the egg whites. If desired, sprinkle a bit of paprika onto each egg. Let chill for at least an hour before serving.