Place the eggs in a single layer in the bottom of a large pot. Add cold water to a depth of an inch or two above the eggs then set the pot over high heat. Once the eggs come to a full boil, cover the pot and turn off the burner. Let the eggs sit for 15 minutes. Transfer the eggs to a bowl of ice water and let sit another 15 minutes.
Once the eggs have fully cooled, carefully peel them. (If the shells are being stubborn, try peeling them under cool running water.) Using a sharp knife, slice the eggs in half. Remove the yolks and place in a small bowl; set aside the empty white halves.
Using a fork, mash the yolks. Add the vinegar, mustard, and mayonnaise and mix until smooth. Season to taste with salt and pepper.
Fill the empty egg white halves with the yolk mixture. Chill the eggs, then sprinkle with paprika before serving.