Put eggs in a single layer in a saucepan and cover with cold water by about 1 inch. Bring to a full boil, cover, remove from heat and let stand 12 minutes for large eggs. Yolks and whites must be firm; allow a little more time if needed.

Transfer eggs to ice water for 10 minutes, then gently crack and peel. Rinse away shell pieces and pat dry.

Halve eggs lengthwise. Remove yolks to a bowl, keeping the whites intact. Mash yolks into fine crumbs with a fork, or press through a fine sieve for a smoother filling.

Mix in mayonnaise, mustard, vinegar, salt and pepper until smooth. Taste and adjust seasoning. If too stiff, add another half teaspoon mayonnaise at a time; the filling should hold a soft peak.

Spoon or pipe the filling evenly into the 12 white halves. Dust with paprika and add chives if using. Cover and refrigerate until serving.

Refrigerate promptly at 40°F (4°C) or below. For best quality use within 2 days and never later than 3–4 days after preparation. Discard after more than 2 cumulative hours out of refrigeration, or 1 hour above 90°F (32°C).