In Large saucepan, cover the eggs with cold water; make sure the water is a good inch above the eggs. Add in the vinegar and bring to a rapid boil. Cover the saucepan and remove it from the heat. Let stand for 15 minutes. Drain the water from the eggs and cool them under cold running water. Shake the pan vigorously to crack the shells. Let the eggs cool in the water.
Shell the eggs and halve them lengthwise. Coarsely chop half the egg whites and transfer to a large bowl. Add the remaining white and all of the yolks to a food processor along with the mayo and mustard. Process until smooth. Scrape the mixture into a bowl and blend with the chopped egg whites. Season with salt and pepper. Can be made ahead and refrigerated overnight.
Serve with crackers of any kind or with wheat chips. Delicious.