Boil the eggs. Place eggs in a single layer in a medium saucepan and cover with cold water by 1 inch. Bring to a rolling boil over medium-high heat. Once boiling, reduce heat to a gentle simmer and cook for 9–11 minutes (11 minutes for fully set yolks).
Ice bath. Use a slotted spoon to transfer the eggs to a bowl of ice water. Let them chill for at least 5 minutes — this stops the cooking and prevents the gray-green ring around the yolk.
Peel. Gently tap each egg all over, roll on the counter to crack the shell, and peel under cool running water.
Halve and separate. Slice each egg in half lengthwise with a sharp knife (wipe the blade between cuts). Pop the yolks into a mixing bowl. Arrange the whites on a serving platter.
Make the filling. Mash the yolks with a fork until crumbly. Add mayonnaise, Dijon mustard, vinegar, salt, and pepper. Stir until smooth and creamy. Taste and adjust seasoning. For a silkier filling, pulse in a mini food processor or press through a fine-mesh sieve.
Fill the whites. Transfer the filling to a piping bag with a star tip (or a zip-top bag with the corner snipped off) and pipe into each egg-white half. A small spoon works too.
Garnish. Dust the tops with smoked paprika and sprinkle with fresh herbs.
Chill and serve. Refrigerate for at least 20 minutes before serving so the filling firms up. Serve cold.