Place eggs in a single layer in a saucepan and cover with enough water that there's 1 1/2 inches of water above the eggs. Heat on high until water begins to boil, then cover, turn the heat to low, and cook for 1 minute. Remove from heat and leave covered for 14 minutes, then rinse under cold water continuously for 1 minute.
Crack egg shells and carefully peel under cool running water. Gently 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. Add mayonnaise, vinegar, mustard, salt, and pepper, and mix well.
Evenly disperse heaping teaspoons of the yolk mixture into the egg whites. Sprinkle with paprika and serve.
Recipe courtesy of Mary Nolan