Place the 6 eggs in a single layer in a medium saucepan. Cover with cold water by at least 1 inch. Bring to a full boil over medium-high heat, then reduce heat to a gentle simmer and cook for exactly 11 minutes.

While eggs cook, prepare an ice bath: fill a large bowl with cold water and plenty of ice. When the 11 minutes are up, transfer the eggs immediately to the ice bath using a slotted spoon. Let them sit in the ice bath for at least 15 minutes to stop cooking completely.

Gently crack and peel the cooled eggs under cold running water — the water helps the shell slide off cleanly. Pat dry with a paper towel.

Slice each egg in half lengthwise with a sharp knife. Carefully pop the yolks out into a medium mixing bowl and arrange the whites cut-side up on a serving platter.

Using a fork, mash the yolks thoroughly until no large lumps remain. For an ultra-smooth result, press the yolks through a fine mesh sieve into the bowl.

Add the mayonnaise, yellow mustard, apple cider vinegar, salt, and black pepper to the mashed yolks. Stir well until completely combined and very smooth. Taste and adjust seasoning — add a tiny pinch more salt or a few more drops of vinegar if needed.

Transfer the filling to a piping bag fitted with a star tip, or spoon it into a zip-lock bag and snip off one corner. Pipe or spoon the filling generously into each egg white half.

Dust the filled eggs with smoked paprika using a small fine mesh sieve or simply a pinch between your fingers. Top with fresh snipped chives if using. Serve immediately or refrigerate uncovered for up to 2 hours before serving.