Step 1: Place eggs in a single layer in a medium saucepan and cover with at least 1 inch of cold water.
Step 2: Bring the water to a full rolling boil over high heat, then immediately remove the pan from the heat and cover with a lid.
Step 3: Let the eggs sit in the hot water for exactly 12 minutes to ensure perfectly cooked yolks.
Step 4: Transfer the eggs to a large bowl of ice water and let them cool completely for at least 5-10 minutes.
Step 5: Gently crack the eggshells and peel them under cool running water; pat dry with a paper towel.
Step 6: Slice the eggs in half lengthwise and carefully remove the yolks into a small mixing bowl.
Step 7: Mash the yolks with a fork until no large lumps remain, then stir in the mayonnaise, mustard, and vinegar.
Step 8: Season the mixture with salt and pepper to taste, mixing until the filling is completely smooth and creamy.
Step 9: Spoon or pipe the yolk mixture into the empty egg white halves.
Step 10: Garnish with a sprinkle of smoked paprika and fresh chives before serving cold.