Boil the eggs: Start by placing the eggs in a saucepan, then cover them with cold water. Bring the water to a gentle boil over medium-high heat. Once boiling, reduce the heat and let them simmer for about 10-12 minutes. After that, carefully transfer the eggs into an ice water bath for at least 5 minutes to cool down.
Peel and slice: Once the eggs are cool enough to handle, peel off the shells and slice each egg in half lengthwise. Gently remove the yolks and place them in a mixing bowl, setting the empty egg whites aside on a plate.
Make the filling: Using a fork, mash the yolks until smooth and crumbly. Add in the mayonnaise, mustard, vinegar, salt, and pepper. Stir everything together until the filling is creamy and well combined. Taste and adjust seasoning as needed if you like a bit more tang, add a little extra mustard or vinegar.
Stuff the eggs: Spoon the yolk mixture into the hollowed-out egg whites. For a more polished look, consider using a piping bag or a resealable plastic bag with the corner cut off. Fill each egg white generously with the creamy mixture.
Garnish and serve: Sprinkle the tops of the deviled eggs with paprika for a bit of color and smoky flavor. If desired, add a sprinkle of fresh herbs like chives or parsley for a touch of freshness.