Place the eggs in a single layer in a large pot and cover with cold water by 1 inch (2.5 cm). Bring to a full boil over high heat.
Turn off the heat, cover and let the eggs sit in the hot water for 12 minutes.
Move the eggs to a bowl of ice water for at least 10 minutes.
Peel under cool running water, pat dry and cut in half lengthwise.
Mash the yolks with a fork until fine. Stir in the mayonnaise, mustard, vinegar, salt and pepper until smooth. Taste and adjust.
Spoon or pipe the filling into the whites.
Top with diced red pepper or paprika and chopped chives or dill. Chill until serving.