Fill a saucepan about a quarter of the way with cold water. Place the eggs in a single layer at the bottom of the saucepan. Add more water so that the eggs are covered by an inch or two of water.
Heat the pot on high heat and bring the water to a full rolling boil.
Turn off the heat, keep the pan on the hot burner, cover, and let sit for 12 minutes.
Strain the water from the pan and run cold water over the eggs or place in a bowl of ice water to cool them quickly and stop them from cooking further.
Crack and carefully peel the eggs under running water. 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.
Spoon prepared yolk mixture into the egg whites and sprinkle with smoked paprika.