Place eggs in a single layer in a saucepan. Cover with enough water so there's at least one inch above the eggs. Bring to a boil, cover, then turn off heat and allow to sit for 15 minutes. Immediately add cooked eggs to ice bath for at least one minute.
Gently crack egg shells and carefully peel the eggs. Pat eggs dry with a paper towel if needed.
Using a sharp knife, slice eggs in half lengthwise. Gently remove yolks and add to medium bowl, and reserve egg whites on a serving platter.
Mash the egg yolks using a fork. Add mayonnaise, mustard, vinegar, salt, and pepper and mix until smooth.
Using a spoon or pastry bag, disperse egg yolk mixture into egg white cups. Sprinkle with paprika and serve.