In a large saucepan, cover the eggs with water, add the vinegar and bring to a rapid boil. Cover the saucepan and remove it from the heat; let stand for 15 minutes. Drain the eggs and cool them under cold running water, shaking the pan vigorously to crack the shells. Let the eggs cool in the water.
Once the eggs have cooled, shell the eggs and halve them lengthwise. Coarsely chop half of the egg whites and transfer them to a large bowl for later use. Add the remaining whites and all of the yolks to a food processor along with the mayonnaise and mustard and process until smooth. Scrape the mixture into a bowl and stir in the reserved chopped egg whites. Season with salt and pepper to taste. Transfer to your serving bowl and dust with paprika.