Place the eggs in a single layer in a medium saucepan and cover with cold water by at least one inch.
Bring the water to a rolling boil over high heat, then immediately cover the pot and remove it from the heat source.
Let the eggs sit in the hot water for exactly 12 minutes to achieve a perfectly set yolk.
Transfer the eggs to a bowl filled with ice and cold water, allowing them to chill for 5 to 10 minutes.
Gently crack the shells and peel the eggs under cool running water, then pat them dry with a paper towel.
Slice each egg in half lengthwise and carefully remove the yolks, placing them into a small mixing bowl.
Add the Greek yogurt, Dijon mustard, apple cider vinegar, sea salt, and black pepper to the yolks.
Mash the mixture with a fork or whisk until it is completely smooth and creamy.
Spoon the yolk mixture back into the egg white halves, or use a piping bag for a more polished look.
Garnish each egg with a light dusting of smoked paprika and a sprinkle of finely chopped fresh chives before serving.