Place eggs in a single layer in a saucepan and cover with cold water by 1 inch. Bring to a rolling boil over medium-high heat. Once boiling, remove from heat, cover, and let stand for exactly 12 minutes.
Immediately transfer eggs to an ice bath and cool for 15 minutes. This quick temperature change prevents further cooking and makes peeling significantly easier.
Gently tap each egg on a hard surface, creating small cracks all around. Start peeling from the wider end where there's usually an air pocket. Peel under cool running water to help separate the shell from the egg white cleanly.
Slice eggs lengthwise with a sharp knife, wiping the blade between cuts for clean edges. Carefully remove the yolks and place them in a medium bowl. Arrange the whites on your serving platter.
Mash the yolks with a fork until completely crumbled. Add mayonnaise, mustard, and vinegar, then mix until smooth and creamy. Season with salt and pepper to taste.
Transfer the filling to a piping bag fitted with a star tip, or use a plastic bag with the corner snipped off. Fill each egg white half with the yolk mixture. Sprinkle with paprika and optional chives just before serving.