Cook the eggs:
Place the eggs in a saucepan and cover with water. Bring to a boil over medium-high heat. Once boiling, remove from heat, cover, and let sit for 10–12 minutes.
Cool the eggs:
Transfer the eggs to a bowl of ice water and let cool for at least 5 minutes. Peel the eggs once cooled.
Prepare the filling:
Slice the eggs in half lengthwise and carefully scoop out the yolks into a mixing bowl. Set the egg whites aside on a serving plate.
Mix the yolk filling:
Mash the egg yolks with a fork until smooth. Add mayonnaise, Dijon mustard, vinegar or lemon juice, salt, and pepper. Mix until creamy.
Fill the egg whites:
Spoon the yolk mixture into the hollowed-out egg whites. For a more polished look, use a piping bag or zip-top bag with a corner snipped off.
Garnish and serve:
Sprinkle the deviled eggs with paprika and add optional toppings like chopped chives or bacon. Serve immediately or refrigerate until ready to serve.