Place eggs in a single layer in a saucepan and cover with enough water to cover 1 inch above the eggs.
Heat on high heat until water begins to boil, then cover, turn the heat off, and let sit covered for 15 minutes.
Rinse under cold water continuously for 1 minute and then place ice over the top and fill pan with cold water and let sit until eggs are chilled.
Carefully crack and peel eggs under cool running water. Gently pat dry with paper towels.
Slice the eggs in half lengthwise, removing yolks to a medium bowl, and placing the whites on a serving platter.
Mash the yolks into a fine crumble using a fork or pastry blender.
Add mayonnaise, vinegar, mustard, salt, and pepper, and mix well.
Drop heaping teaspoons of the yolk mixture into the egg whites. Sprinkle with paprika and serve.