Place the eggs in a saucepan, cover with cold water by about an inch, and bring to a boil. Turn off the heat, cover, and let sit for 12 minutes.
Transfer the eggs to a bowl of ice water and let cool for at least 10 minutes before peeling.
Peel the eggs and slice in half lengthwise. Remove the yolks to a bowl and set the whites aside on a serving plate.
Mash the softened butter into the warm yolks with a fork until smooth.
Add the mayonnaise, mustard, vinegar or pickle juice, nutmeg, salt, and pepper. Stir until completely smooth, tasting and adjusting as needed.
Spoon or pipe the filling into the egg white halves.
Sprinkle with smoked paprika and chopped chives. Refrigerate for at least 30 minutes before serving.