Place eggs in a large stockpot or pan (that has a lid); fill with cold water, making sure the water covers the eggs 1-2 inches. Add 1 tablespoon of vinegar to the water. Turn stove on high heat, and bring the water to a boil. As soon as the water begins to boil, cover pot and turn heat off. Allow eggs to sit in water for 12 minutes, with the lid still on the pot. Remove eggs from pot using a slotted spoon, and place on a paper towel or clean kitchen towel.
When eggs are cool, peel and slice eggs in half lengthwise, and remove the yolks. Mash yolks with a fork and add mayonnaise, mustard and salt. Put the yolk mixture into a plastic baggie and snip the end off one corner. Pipe the mixture into the whites. Sprinkle with paprika, if desired. Cover and chill for at least one hour.